Combine 1/2 cup flour, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Dredge chicken in flour mixture, coating well. Sauté in butter in a large skillet until golden brown. Transfer chicken to a shallow 2-quart casserole, and add water to cover. Reserve pan drippings in skillet; set aside. Bake chicken at 350° for 50 minutes or until tender. Remove chicken to serving platter, and keep warm.
Add 3/4 cup half-and-half to pan drippings, stirring until smooth. Combine remaining half-and-half and 1 tablespoon flour, mixing well. Stir into pan dripping mixture. Cook mixture over medium heat, stirring constantly, until thickened and bubbly. Stir in salt and pepper to taste. Serve gravy over chicken.