Preheat oven to 325 degrees F. Put a large kettle of water on to boil.Advertisement
Combine sugar and 1/4 cup water in a small saucepan. Bring to a simmer over medium heat, stirring occasionally. Increase heat to medium-high and cook, without stirring, until the syrup turns a deep amber color, 5 to 7 minutes. Immediately pour the syrup into a 2-quart soufflé dish and carefully tilt so that the caramel coats the bottom and halfway up the side.
Whisk eggs, egg whites, condensed milk, milk and vanilla in a large bowl. Strain the mixture through a fine sieve into the caramel-coated dish. Set the dish inside a larger ovenproof pan, such as a large Dutch oven or small roasting pan. Very carefully pour enough very hot water into the larger pan to come about halfway up the sides of the of the flan dish.
Bake until the custard is set around the edges but still jiggly in the center, 1 to 1 1/4 hours. Transfer the flan dish to a wire rack. Let cool at room temperature for 1 hour. Cover and refrigerate until very cold, at least 4 hours or up to 1 day.
To serve, run a knife around the inside of the dish and invert the flan onto a serving plate.
To make ahead: Refrigerate for up to 2 days.
Equipment: 2-quart soufflé dish
3 other carbohydrate, 1/2 medium-fat protein