Dice the corned beef into chunks, and heat the oil in a large skillet to high.
Add the beef to the skillet and cook until lightly browned.
Add in the onion, peppers, and potatoes and combine. Season well, then leave them alone!
Cook for about 5 minutes, until a brown crust forms on the bottom.
Continue to cook, stirring until the potatoes are cooked through and you have lots of browned bits. Check for seasoning and adjust if necessary.
Remove from the heat, and add the cheese slices to the top, and let them sit while you cook the eggs.
Cook the eggs to your liking, and serve on top of the hash/cheese mixture.