Meanwhile, heat the butter in a nonstick skillet over medium-high heat. Fry the eggs sunny-side up or over easy; season with salt and pepper.
Place the cheese slices on top of the hash, reduce the heat and let sit until the cheese melts, about 1 minute. To serve, top each portion of hash with a fried egg.
2 tablespoons vegetable oil
8 ounces cooked corned beef, diced
1 white onion, finely chopped
1 bell pepper, finely chopped
2 medium baking potatoes, peeled and shredded (about 2 cups)
4 tablespoons unsalted butter
4 large eggs
Kosher salt and freshly ground pepper
4 slices cheddar cheese (about 2 ounces)