Preheat oven to 325 F. Arrange 6 ramekins in a deep baking dish.
Bring the cream to a gentle boil. Remove from heat and add chocolate. Let stand for 30 sec, then whisk until smooth.
Whisk together egg yolks, sugar and vanilla. Whisk about 1/2 cup of the chocolate mixture into the yolks, then whisk this mixture into the remaining chocolate mixture. Pass the mixture through a fine-mesh sieve into a measuring cup with a pouring spout. Divide the base among the ramekins. Pour enough hot water into the baking pan so it comes almost halfway up to the sides of the ramekins. Bake for about 25 minutes, or until the custards are set around the edges and slightly jiggly in the center.
Transfer the ramekins to a wire rack and let cool completely.
Refrigerate the custards for at least 4 hours before serving whipped cream.