Melt the butter in a ten-inch skillet. Add the tomatoes, celery, garlic, onion, green pepper, salt, sugar and black pepper. Mix well. Remove from the heat.
Wash and trim the broccoli. Place over the vegetables in the skillet. Cover tightly and cook over medium heat for fifteen to twenty minutes, until tender.
Place the broccoli on dinner plates. Stir the cornstarch into the juice and vegetables left in the pan. Cook until slightly thickened. Discard the garlic. Serve a spoonful of the sauce over each serving of broccoli.