In a large pot, stew first six ingredients in 2 quarts of water for about 30 minutes; drain, allow to cool to touch, and then shred chicken. Place ingredients in a 9-x-13-inch baking dish.
Combine next nine ingredients and pour over chicken mixture. Top with cracker crumbs; drizzle melted butter over top. Bake at 350ยบ for 25 minutes. Remove from oven and sprinkle cheese over top; bake another five minutes.