Preheat oven to 400 degrees F (200 degrees C). Butter an 8-inch square baking dish.
Melt 3 tablespoons butter in a saucepan over medium heat. Cook and stir scallops in melted butter until lightly browned, about 5 minutes. Stir flour into scallop mixture until dissolved, 2 to 3 minutes.
Gradually pour half-and-half and milk into scallop mixture, while stirring constantly until milk mixture is thickened, 5 to 10 minutes; season with salt and pepper. Pour scallop mixture into the prepared baking dish.
Place remaining 2 tablespoons butter in microwave-safe bowl and heat in microwave until melted, 15 to 20 seconds. Stir bread crumbs into melted butter until coated; sprinkle over scallop mixture.
Bake in the preheated oven until bread crumbs are browned, about 10 minutes.