Drizzle butter over bread cubes in a large bowl; sprinkle with cheese, and toss well.
Combine broccoli and next 5 ingredients in a large bowl. Spoon filling into a lightly greased 2-qt. rectangular or oval baking dish or individual baking dishes; top with bread cubes.
Bake, uncovered, at 400° for 30 minutes (20 to 25 minutes for individual cobblers) or until bubbly and top is toasted.