In a shallow bowl, whisk egg and egg white until foamy. Whisk in milk, vanilla, cinnamon, and nutmeg.

Have warming drawer heated or heat oven to 200°.

Heat butter in heavy skillet over medium-low heat. Dip 4 slices of bread in the egg mixture, turning to coat thoroughly. Let excess drip back into bowl.

Place coated bread slices in hot skillet. Cook, turning, until both sides are nicely browned, about 2 minutes each side.

Transfer to a warm plate and keep warm in oven. Repeat with remaining bread and egg mixture. To serve, sprinkle with cinnamon sugar, if desired. Serve with maple syrup.