Preheat the oven to 375°F. Cut a 3 to 4-inch wide hole in the tops of the rolls and hollow out. Brush the insides of rolls with melted butter and add 1 tablespoon Beemster Gouda to each roll. Cut each ham slice in half and use both halves to line each roll. Carefully crack an egg into each roll.

Arrange rolls on baking sheet and cover them loosely with aluminum foil. Bake for 20 minutes or until the eggs are set. Sprinkle each roll with 1 tablespoon Beemster Gouda. Bake for 3 minutes or until Beemster is melted and the eggs are desired doneness.