Baked Eggs with milk

7 eggs 1 cup milk 2 teaspoons sugar 1 lb grated monterey jack cheese (or Muenster cheese) 4 ounces cream cheese , cubed (room temperature) 1 (16 ounce)[...]

1 small onion , minced 1 red bell pepper , 1/4-inch dice 1 green bell pepper , 1/4 inch dice 5 large mushrooms , 1/4-inch dice 2 tablespoons unsalted butter[...]