Brown beef with onion, green pepper, ½ teaspoon salt and pepper in a 12-inch skillet or electric skillet over medium heat. Remove meat mixture from skillet; drain fat. Reduce heat to low. Melt butter in skillet. Spread potatoes over butter and sprinkle with remaining salt. Top with beef mixture. Combine eggs and milk; pour over all. Cook covered until potatoes are tender (about 30 minutes). Top with cheese, cover and heat until cheese is melted (about five minutes). Yields 4 to 6 servings.