Heat milk in 1-quart saucepan over low heat until hot; do not boil. Beat eggs, egg whites and sugar in medium bowl with electric mixer at medium speed 5 minutes or until slightly thickened. Gradually beat in milk and vanilla.
Pour milk mixture into 1 1/2-quart souffle dish or casserole; sprinkle lightly with cinnamon and nutmeg, if desired. Place souffle dish in roasting pan and place on oven rack; pour 2 inches hot water into roasting pan.
Bake, covered, 40 to 50 minutes or until knife inserted halfway between center and edge of custard comes out clean. Cool to room temperature on wire rack. Cover; refrigerate 3 to 4 hours or until chilled.
When ready to serve, press brown sugar through a sieve over custard. Broil 4 inches from heat 2 to 3 minutes or until sugar is melted and caramelized. Serve immediately.