Steam cabbage and onion in a small amount of water until tender. Add the ham. Place into a buttered baking dish.
In a skillet, melt butter over low heat. Stir in flour until smooth. Add milk, stirring until smooth. Add salt, cheese and stir until melted. Pour over the cabbage mixture. Sprinkle with bread crumbs and dot with butter. Bake for 30 minutes.
