How to Make It
In a medium saucepan, cover the potatoes with water and boil until the potatoes are just tender, about 20 minutes. Drain and let cool slightly. Finely chop the potatoes.
In another saucepan, cover the beets with water and boil until tender, about 20 minutes. Drain and let cool slightly, then peel and finely chop the beets.
In a large bowl, toss the potatoes and beets with the corned beef, onion and chile powder and season with salt and pepper.
In a large cast-iron skillet, melt the butter until foamy. Add the corned beef mixture and cook over moderate heat without stirring until golden and crusty on the bottom, about 10 minutes. Using the back of a large spoon, make 6 evenly spaced pockets in the hash. Crack an egg into each depression, cover the skillet and cook until the eggs are just set, about 5 minutes. Serve immediately.