Combine first 3 ingredients, beating well; gradually add milk, stirring constantly. Stir in vanilla. Pour into eight 6-ounce custard cups. Sprinkle with nutmeg.
Place custard cups in a 13- x 9- x 2-inch baking dish; pour hot water into pan to a depth of 1 1/2 inches. Bake at 325° for 50 minutes or until knife inserted halfway between center and edge of custard cup comes out clean. Remove cups from water; cool. Unmold and serve with Rum Sauce.