Combine corned beef hash, onion, and bell pepper in an ovenproof skillet. Cook, stirring occasionally, over medium-high heat until vegetables begin to soften and hash begins to brown, 10 to 15 minutes. Make 4 indentations in the hash for the eggs. Remove from heat.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Carefully crack an egg into each indentation. Top with chopped tomatoes.
Place skillet under broiler; broil until eggs are cooked to preferred doneness, 4 to 10 minutes. Check often to avoid burning eggs. Remove skillet from oven. Top with shredded cheese; sprinkle with salt and pepper.