Preheat the oven to 350°. Line a baking sheet with parchment paper.
In a small heavy saucepan, cook 2/3 cup of the sugar over moderately low heat without stirring until melted and deep golden, about 12 minutes. Working quickly, pour about 1 tablespoon of the caramel into each of four 2/3-cup ramekins. Drizzle the remaining caramel over the parchment and let stand at room temperature to harden.
In a bowl, whisk the eggs with the egg whites and the remaining 1/3 cup sugar until combined. In a small saucepan, warm the evaporated milk and coffee over moderate heat until steaming, about 3 minutes. Let stand for 1 minute. Whisk the steamed milk into the egg mixture, then whisk in the cream and vanilla.
Strain the coffee custard, then pour it into the ramekins and set them in a baking dish. Add enough cold water to the dish to reach three-quarters of the way up the sides of the ramekins. Bake for about 35 minutes, or until the custards are almost set. Let cool in the water bath. Cover and refrigerate the crème caramels until chilled, at least 2 hours or overnight. (The caramel pieces can stand at room temperature, covered, overnight.)
To serve, dip the bottom of each ramekin in hot water, then run a knife around each crème caramel and invert onto individual plates. Break the reserved hardened caramel into large pieces and arrange them decoratively around the custards.
One Serving Calories 373 kcal, Protein 13 gm, Carbohydrate 62 gm, Cholesterol 130 mg, Total Fat 8.2 gm, Saturated Fat 4.3 gm.