In a large skillet over medium heat, melt 1½ tablespoons of butter until it begins to bubble. Add peppers and onions. Cook until translucent, about 5 minutes. Transfer sauteed onions mixture to a small bowl.
Add remaining butter to the skillet and stir in corned beef and potato cubes. Fry corned beef mixture for 5 minutes, without stirring, until potatoes and beef are crispy and golden brown on the bottom. Stir hash and cook another 5 minutes.
Optional Egg: If poaching the eggs with the hash, fluff up hash mixture and make 4 wells of hash in the skillet. Place 1 teaspoon butter in each well and then place 1 egg on top of the butter.
Cover and cook over medium low heat until eggs have cooked to your preference.Alternatively, you can make a fried egg sunny side up in a separate skillet and serve it over the hash.