Heat a large, nonstick skillet over medium-low heat. Melt the butter and add the olive oil, then add the smoked and sweet paprika and cook until fragrant, about 30 seconds. Add the eggs to the middle of the pan. Cook, undisturbed, until the eggs begin to set, about 30 seconds.
Using a rubber spatula, pull the edges of the set eggs toward the middle of the pan, allowing the raw egg to run out to the edges. Continue with this method until the eggs are mostly cooked. Either flip the eggs in the pan by sheer strength and wrist power or slide the eggs onto a plate and invert them back into the pan. Immediately remove from the heat and cover to keep warm.
Heat another nonstick pan over medium heat. Lay the tortillas in the pan and top with lots of shredded cheese. Cook until the tortillas are heated through and the cheese begins to melt. Flip the tortillas. Cook, cheese side down, until it's melted and crispy, 1 to 1 1/2 minutes. Using a spatula to release the cheese, remove the tortillas from the pan.
Divide the eggs and avocado among the tortillas. Season with salt and serve with hot sauce or a squeeze of lime juice.