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Preheat oven to 350 degrees. Boil water in a 4-quart saucepan and reserve for water bath.
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Heat 2/3 cup sugar with the cold water on medium heat, stirring occasionally, until the sugar is dissolved and appears a light caramel color.
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Whisk together eggs, egg whites, and remaining sugar in a separate bowl until well blended. Add milk and vanilla and beat.
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Divide mixture into 8 custard cups.
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Place cups in a large roasting pan and pour boiling water in pan until cups are halfway immersed in water.
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Bake for 40 minutes, until center of custard is just set.
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Remove from oven and place cups out of water on a wire cooling rack.
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When custards are cooled, place in refrigerator, covered, for 4 hours.
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Invert cups onto plates and let cups sit above custard for several minutes. Remove cups from custard just before serving.