In a large saucepan, melt 2 tablespoons butter. Stir in flour and salt. Add milk and stir until bubbly. Add cheese, and stir until all of the cheese is melted. Stir in potatoes and heat thoroughly.
Pour half of the mixture into a 10x6 inch baking dish.
Cook broccoli according to package instructions; drain well. Layer broccoli over the potatoes in the baking dish. Pour the remaining potato mixture over the broccoli. Sprinkle the bread crumbs and 1 tablespoon melted butter over the top of the casserole.
Bake at 350 degrees F (175 degrees C) for 20 to 35 minutes; or until bubbly and browned lightly.