Heat a cast-iron skillet over medium-high heat until hot, then swirl in butter or oil. Add potatoes. Let cook, without stirring, until crusty underneath, about 6 minutes. Turn with a thin spatula and cook, until starting to brown on other side, 3 to 4 minutes. Add meat with its vegetables and cook until hash is as crisp as you like, 10 to 15 minutes).
Meanwhile, in a separate pan, fry however many eggs you want. Spoon hash into bowls. Slide an egg on top of each, sprinkle generously with minced chives, and serve with your favorite hot sauce.