Place sugar in a 9-inch cast iron skillet; cook over medium heat, stirring constantly with a wooden spoon, until sugar dissolves and becomes a golden syrup. Gradually pour syrup into milk in a large mixing bowl, beating constantly, until syrup dissolves in milk. Stir in breadcrumbs, eggs, salt, nutmeg, butter, and vanilla.
Pour mixture into a greased 1 1/2-quart casserole. Place casserole in a 13- x 9- x 2-inch baking pan; pour hot water into pan to a depth of 1/2 inch. Bake, uncovered, at 350° for 1 hour or until lightly browned. Spoon into individual serving bowls, and serve warm with sweetened whipped cream.