PREHEAT oven to 325°F. Microwave white chocolate, milk, sugar and butter in large microwaveable bowl on HIGH 4 min. or until butter is melted, stirring after 2 min. Stir until chocolate is completely melted. Add eggs and vanilla; beat with wire whisk until well blended.
POUR over bread cubes in 2-qt. baking dish. Place dish in larger baking pan, then place in oven. Carefully add enough boiling water to baking pan to come 1 inch up side of baking dish.
BAKE 40 to 45 min. or until knife inserted in center comes out almost clean. Serve warm with the Chocolate Sauce.