In a large skillet, saute onions in butter. In a bowl, lightly beat eggs and milk; pour over onions. Cook over medium heat; as the eggs set, lift edges, allowing uncooked portion to flow underneath.
When eggs are nearly set, spoon corned beef hash over top of omelet. Sprinkle with cheese and pepper. Remove from heat; cover and let stand for 1 to 2 minutes or until cheese is melted. Place on serving plate and cover with tomato slices. Cut into wedges to serve. Makes 4 to 6 servings. Enjoy!