For caramel syrup, in a heavy medium-size skillet, cook the 2/3 cup sugar over medium-high heat (don't stir) until the sugar begins to melt, shaking saucepan occasionally. Reduce heat to low and cook until syrup is golden brown, stirring frequently.
Divide the caramel syrup among six 6-ounce custard cups, tilting cups to spread syrup. Set cups in a 13x9x2-inch (3-quart rectangular) baking dish. Allow to stand for 10 minutes.
Meanwhile, for custard, in a mixing bowl, stir together eggs, milk, half-and-half or light cream, the remaining 2/3 cup sugar, and the vanilla. Pour into the caramel-coated custard cups. Set pan with custard cups in oven on rack. Pour boiling water into the dish around custard cups to a depth of 1 inch.
Bake in a 325 degree F oven for about 45 minutes or until a knife inserted near centers comes out clean. Remove custard cups from baking dish and cool on wire rack. Cover; refrigerate for at least 3 hours.
To serve, loosen edges of custard cups with a spatula or knife, slipping point of spatula down sides to loosen; invert onto dessert plates. Makes 6 servings.
Prepare custards up to 24 hours ahead. Cover and refrigerate.