The irony of a lactose-intolerant guy opening an ice cream shop is not lost on Sameh Wadi.

But the gifted chef — he’s the culinary talent behind Saffron Restaurant & Lounge in downtown Minneapolis and World Street Kitchen (WSK) in the city’s Lyn-Lake area — doesn’t let obstacles get in the way of success.

Or innovation. The Milkjam Creamery scoop case features 16 flavors, boasting catchy, gotta-tweet-these names, as well as flavors that are a far cry from the Rocky Roads and Praline Pecans of the world. Nearly half are vegan, and most are gluten-free.

Crowds have followed to the slick-looking shop, located next door to WSK. And how. The line that frequently snakes out the door has quickly become one of the city’s most Instagrammed images, probably topping the Walker Art Center’s “Spoonbridge and Cherry.”

Wadi took a few minutes recently to talk ice cream. Here’s his take on …

Being lactose-intolerant: “It doesn’t stop me. I’m willing to pay the price, because ice cream is one of the only things that I’m truly addicted to. At home, my refrigerator might have some soy milk, maybe some eggs, and probably some old, almost rotten vegetables. But there’s always four or five kinds of ice cream in the freezer. I’m an addict. I don’t discriminate, either. It goes from Ben & Jerry’s to Jeni’s. Of the small producers, Sweet Science is my favorite; I absolutely love her [owner Ashlee Olds]. I figured that when I opened Milkjam, it would stop. But, if anything, it’s worse, because I can bring it home with me. All the test batches end up at home. I should take a picture of my freezer, because it’s hilarious.”

Nondairy ice creams: “I’ve never liked them, at least the commercially made ones. They always felt like they were missing something. Namely, the fat. You don’t get the satisfaction, you know? And I’m not about to eat something that isn’t delicious. Sorbets are good, but they don’t satisfy that craving for the fat. And I definitely crave the fat.

“Our plan is to do 50 percent of our ice creams as dairy-free. We’re at about 40 percent right now.

“We use different milks for different things, but most of them have coconut milk; that gives them the right texture. Then we add in plant-based fats. That makes it rich, without having to use chemicals or thickening agents or emulsifiers. We use all-natural ingredients. Pretty much any plant-based fat that you can think of, I put in ice cream: olive oil, peanut oil, coconut oil, cocoa butter, avocado oil. We’ve experimented with a whole slew of things.”

The shop’s amazing dark chocolate vegan ice cream, called Black: “That one is going to have its own Twitter account pretty soon. It’s really set a trend, because now we’re seeing black ice creams all over the country. To be honest, I just wanted a really rich dark chocolate ice cream, and I wanted it to be vegan. It’s brilliant, really, because if there’s no dairy, there’s nothing to mask the flavor of the chocolate. It’s made with coconut and almond milks. We use four kinds of chocolate, and add black cocoa to make it earthier. In the test batch, we put in the wrong amount of black cocoa, and it came out jet black. This was two days before we opened, and we thought, ‘Oh, no, we screwed up. What are we going to do?’ But then we tasted it and we were like, ‘Wow, this is really good.’ We ended up slightly tweaking the recipe, and it’s really all about that unadulterated chocolate flavor.”

The shop’s remarkable namesake flavor, a blend of caramelized goat, cow and condensed milks: “The idea came from combining tres leches [three types of milk] and cajeta [caramel-like mixture]. Our opening pastry chef, Ben Spangler, he got the job by bringing a variation of it to his interview. I took one taste and I knew that this was it, and that he was the guy. Unfortunately, things didn’t work out between us, and we wish him the best. We have a new team: Sean Little and Jaclyn Von, and they’re great. But Milkjam is Ben’s flavor, and it’s brilliant. All we did was add condensed milk to it, to make it a little more chewy and give it a little more body. That made it more about the milk, and less about the cajeta.”

Top-selling flavors: “We’re constantly switching flavors in and out. For the traditional ice creams, Ridin’ Duuurty [Oreo milk with Oreo chunks and salted peanut butter] is easily the top seller, and among the vegan ice creams, it’s the Black. We have this new PB v. Everybody. It’s roasted bananas and peanut butter ice cream with chopped-up Oreos. That’s doing really well.”

Attention-getting ice cream flavors: “You’re thinking of the spicy lamb bacon-miso, right? I’ve wanted to do that one for a while. We did a caramelized lamb bacon ice cream at Saffron a few years back, and people kept requesting it. Miso and lamb bacon just work together so beautifully. We add a lot of dark molasses flavor to the miso; that gives it a lot of salty butterscotch flavor, with lots of umami. We caramelize the lamb bacon with sugar and chiles, to give it heat, and that adds even more umami. It’s dynamite. I have a few pints at home. I’m saving them.

“July is National Ice Cream Month, so every week we’re doing a different limited-edition pint. We did a collaboration with Sociable Cider Werks, their Freewheeler cider with an apricot purée. It was vegan, kind of a mashup between a sorbet and Italian ice, and it was so refreshing. I think we’re close to being sold out of that one.”

The wordplay behind the ice cream flavors’ witty names: “Most of them come up between me and Tip Sayarath. She’s our jack of all trades here, and she’s also in charge of our social media. She coined the term Jam Bun [the shop’s ice cream-filled doughnuts]. Duuude was an easy one, because we were just thinking of the munchies [it’s filled with chocolate-covered pretzels, potato chips, Nutter Butter cookies and other goodies] and thinking of what you do when you get the munchies and you say, ‘Duuude, this is so good.’ With the Halle Berry [Greek yogurt, with a blueberry-raspberry-strawberry-blackberry-rose swirl], there’s a funny rap song where a guy screams ‘Halle Berry’ over and over, and because there are these berry swirls in the ice cream base, I was singing that song when I first made it.”

Milkjam’s frequently long (and relatively fast-moving) lines: “It’s humbling to see people waiting in line for food, let alone for my ice cream. People in Minnesota really love their ice cream.

“The ice cream game in Minneapolis is pretty solid. I grew up eating all these great local ice creams — Izzy’s, Sebastian Joe’s — so to have such positive support from the die-hard fans of these ice cream shops, that’s a pretty amazing feeling.

“We’re serving somewhere between 500 and 1,500 people a day, depending upon the day. That’s a lot of ice cream. On weekends, it’s more, and on rainy days, it’s less. We make everything in-house, starting with all of our custard bases. It’s very laborious. We’re 99 percent scratch-made. We’re buying some of the garnishes, and we’re buying the doughnuts for the Jam Buns from Glam Doll. And proudly. Those Glam Doll ladies, I absolutely love them.”

Milkjam’s jumbo-size scoops: “They’re big for the price, and for the quality of the ingredients. My margins are really slim. I’m learning how to run an ice cream shop. I never said I was a smart businessman.”

Alcohol-fueled ice cream sodas: “We’re just trying to do something outside the realm of a normal scoop shop. It’s something a little more adult. The main focus of so many ice cream shops is kids, so we wanted a place where parents can came in and get their drink on while Johnny gets his ice cream cone. We have a liquor license from World Street Kitchen, so it’s a perfect thing to be able to tack on.

“The Champagne we use is super-dry; it really cuts through the sweetness of the ice cream. It’s not a sugar bomb. It goes really goes well with the Hibiscus Lemonade [Italian ice] flavor. The raspberry lambic we’re using pairs well with richer flavors. We pour it over the Milkjam; that’s my go-to recommendation right now. For beer, we have that black ale [from Duluth’s Bent Paddle Brewing Co.], and even though it’s not super seasonally appropriate, I recommend it with the Black ice cream. It really pairs beautifully with those cocoa notes.”

His projections for winter: “I’m hoping that the momentum will continue, since World Street Kitchen is right next door. We have that built-in clientele coming through the door already. Besides, you go to a lot of ice cream shops in the winter, and you still see people there. I’m one of those people.”

The young counter staff: “We get a lot of kids from the neighborhood, and it’s really cool to be a part of the community in such a positive way. They’re super-passionate about what they’re doing. In some cases, it’s their first job, ever. Some of them just blow my mind about how excited they are to learn new things. They really do remind me of me, and of my first job. It’s a fantastic thing to be a part of.”