Spoon cooked rice into greased 3-quart casserole. Layer broccoli over rice. Melt butter in saucepan. Remove 2 T. butter and sprinkle over bread crumbs in a bowl. Set aside.
Saute onion in remaining 4 T. butter. Blend in flour, salt and pepper. Slowly stir in milk. Cook over medium heat, stirring constantly until thickened. Add ham and heat until bubbly. Pour into casserole. Layer cheese over ham mixture. Sprinkle on crumbs. Bake at 350 degrees for 45 minutes.