Set the oven rack about 6 inches from the heat source and preheat the oven's broiler on low.
Add the oil, corned beef hash, onion, and bell pepper in an ovenproof skillet over medium-high heat. Cook, occasionally stirring until vegetables begin to soften and hash begins to brown, 10 to 15 minutes. Make indentations in the hash for the eggs. Remove from heat.
Carefully crack an egg into each indentation. Top with chopped tomatoes and cheese.
Place skillet under broiler; broil until eggs are cooked to preferred doneness, 5 to 10 minutes until the whites are firm. Check often to avoid burning eggs. Remove the skillet from the oven. Season with salt and pepper.
While the eggs are cooking, toast the bread and then spread it with butter.
Portion the skillet and serve with toast and orange juice.