Preheat oven broiler to medium-high heat.
In a medium bowl mix eggs, milk, salt, pepper, butter until well blended; stir in diced peppers.
Cook in a 12-inch ovenproof, non-stick skillet over medium heat until edges are set and eggs begin to cook through, approximately 5 minutes.
Sprinkle shredded mozzarella cheese over eggs and remove from stove; heat under broiler until cheese is melted and eggs are set (1-2 minutes).
Cool for 10 minutes before serving.