Melt the butter in a large uncovered pot. Add the onions, shallots, parsley, and thyme. Cover and cook over low heat, stirring frequently, for 15 minutes or until onions are tender. Add the carrots, celery, potato, wine, tomatoes, and zucchini. Bring to a boil over medium heat, uncovered. Lower the heat, stir in the rice, and simmer, stirring frequently about 1 hour until the rice is cooked.
Stir in the broccoli and continue cooking for 15 minutes. Stir in the milk, cream, Tabasco, salt, and pepper. Taste for seasoning.