Preheat oven to 450 degrees.
Cut off the beet greens and reserve them for another dish, if you wish.
Scrub the beets, toss them with 1 tablespoon olive oil, and spread them in a baking pan. Roast until very tender, 50 to 60 minutes. Let cool slightly, then rub off the skins under running water. Cut into 1/4-inch dice and set aside.
In a 12-inch cast-iron skillet, melt 6 tablespoons butter over medium-high heat. Split ancho chiles and remove the seeds, then cut them into thin strips and add them to the pan with the beets, potatoes and corned beef, and season with salt and pepper. Toss and cook until heated through, about 10 minutes. Add the Worcestershire and cilantro, and reduce heat to low. Once hash is crispy, turn off heat and let it set for 5 to 10 minutes. This will help keep it together when slicing.
Meanwhile, in a 12-inch nonstick pan, heating remaining 1 tablespoon butter and 1 tablespoon olive oil over medium heat. Once it has foamed and subsided, crack the eggs into the pan, season with salt and pepper, and fry to the desired doneness.