In a large skillet, saute the carrots, celery and onion in 3 teaspoons butter until tender. Transfer to a greased 1-1/2-qt. baking dish. Top with 3/4 cup cheese. In the same skillet, saute broccoli in the remaining butter for 1 minute. Place over cheese; pour broth over all.
Cover and bake at 350° for 25 minutes. Uncover; sprinkle with remaining cheese. Bake 5 minutes longer or until cheese is melted and vegetables are tender. Season with salt and pepper. Serve with a slotted spoon.