In a saucepan, cook broccoli and onion in a small amount of water until crisp-tender; drain.
In a greased 1-1/2 quart baking dish, layer the rice, ham and broccoli-onion mixture.
In a small bowl, combine the soup, cheese and milk; spoon over broccoli.
Bake, uncovered, at 350° for 20 minutes.
Meanwhile, coarsely crumble bread. In a skillet, cook crumbs in butter over medium-high heat until lightly browned.
Sprinkle breadcrumbs over casserole. Bake 15 minutes longer or until heated through.
VARIATION: To make things simpler, you could use bread crumbs from a can.