PREPARATION:

To make the caramel:

1. Position the oven rack in the center of the oven, and preheat the oven to 275°F/135ºC. Set six 6-ounce ramekins in a roasting pan. Combine the sugar and water in a heavy medium saucepan. Gently stir over medium-high heat until the sugar dissolves, about 5 minutes. 
2. Boil without stirring until the syrup turns a deep golden brown color, occasionally brushing down the sides of the pan with a wet pastry brush to prevent the sugar crystals from forming, and swirling the pan, about 4 minutes. Once the sugar has dissolved and turned into a liquid, it will begin to color gradually.
3. When the sugar becomes golden brown remove the saucepan from the heat.  Immediately pour the caramel evenly into the bottom of six ramekins, dividing equally. Set aside. The caramel will harden as it cools.

To make the crème custard:

1. Meanwhile, combine the cream, milk and sugar in a heavy medium saucepan, stirring constantly until the sugar dissolves. Bring to a simmer over medium heat then remove from the heat and cool slightly.
2. Whisk the eggs, egg yolks and vanilla in a large bowl by hand to blend.  Once the milk mixture has cooled slightly, about 5 minutes, gradually whisk it into the egg mixture. Strain the custard mixture through a sieve and into a 4-cup measuring cup. 
3. Place the ramekins in a roasting pan. Pour the custard mixture over the caramel in the ramekins, dividing equally.  Transfer the roasting pan to the oven. Pour enough hot water into the pan to come halfway up sides of the ramekins.
4. Bake until the outer 1-inch perimeters of the custards are softly set but the centers are still loose, about 1 hour (the custard will firm up after it is refrigerated). To test whether the crème caramels are ready, push a small knife into the center of one of the dishes, and if the caramel rises out of the hole made by the knife, then they are ready.
5. Remove roasting pan from the oven then remove the crème caramels from the roasting pan.  Refrigerate the crème caramels until cold, at least 2 hours. Cover and refrigerate overnight. Refrigerating the crème caramels overnight allows time for the caramel to dissolve and form a thin sauce when the custards are inverted.

To serve the crème caramels:

1. When ready to serve the crème caramels, run a small sharp knife around the sides of the ramekins to loosen the custards from the ramekins.  Working with one crème caramel at a time, place a plate atop the crème caramel; invert the crème caramel onto the plate. 
2. Shake gently to release the crème caramel from the dish (you will hear it being released).  Carefully remove the dish, allowing the caramel syrup to run over the crème caramel.  Garnish with fresh raspberries and serve.