Place a high-sided skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the meat to the skillet, breaking it up a wooden spoon or potato masher, and cook until caramelized, 6-7 minutes.
Add the garlic, onion, chili powder, cumin, tomato paste, hot sauce, peppers and corn to the pan. Cook until the onion is tender, about 5 minutes. Season everything with salt and pepper, add the stock to the skillet and cook until the liquid has reduced and thickened, about 5 minutes more.
While the hash is simmering, place a large, nonstick skillet over medium heat and melt the butter. Break the eggs into the pan, spacing them about an inch apart. Season the eggs with salt and pepper and cook, flipping once, until the whites have set, about 4 minutes total.
To serve, fill a bowl with a couple spoonfuls of hash, topping it off with some shredded cheese, a fried egg and a garnish of cilantro.