Arrange broccoli in a large steamer basket over boiling water. Cover and steam 5 to 8 minutes or until crisp-tender; remove from basket. Add squash and onion to basket, and repeat procedure.
Combine squash, onion, and butter in a large bowl; mash. Stir in broccoli, eggs, and next 3 ingredients; spoon into two lightly greased 2-quart baking dishes. Sprinkle evenly with breadcrumbs.
Bake at 350° for 20 to 25 minutes or until golden.