Heat the butter in a non-stick pan over medium low heat. Sauté the onion, pepper, and corned beef until the onions and peppers are soft. Season with salt and pepper to taste.
Heat oil in a non-stick pan over medium heat. Once the pan is hot, crack the eggs on a flat surface and into the pan (being careful not to break the yolks). Cook the eggs until the whites are mostly firm for about 2-3 minutes, then gently flip the eggs with a spatula and cook for 30 seconds more. While the eggs are cooking, toast the bread and butter it if desired.
Serve the eggs and corned beef hash with toast and apples.