Preheat oven to 350 degrees. Place butter in a 9x13 inch baking dish and place in oven to melt. Remove from oven.
Place frozen broccoli in hot water to thaw then drain well. Spread broccoli evenly over the melted butter. Top with American cheese slices and then the stuffing mix.
In a small saucepan, combine mushroom soup and evaporated milk and stir until very hot. Pour hot soup over the stuffing mix and bake in preheated oven for 30 to 40 minutes. Makes 12 servings. Enjoy!