Bring a large saucepot of water to a boil over high heat. Preheat oven to 350°F.

Meanwhile, puree 2 cups raspberries and strain through a fine mesh sieve to remove seeds. You should have 2/3 cup seedless puree.

In a small saucepan, heat 2 cups heavy cream, raspberry puree and vanilla just to a simmer. Remove from heat. In a medium bowl, whisk together eggs, egg yolks and sugar. While whisking constantly, slowly add 1 cup cream mixture to egg mixture until blended. Add egg mixture back to cream mixture, whisking until evenly blended.

Evenly divide between 4 (6 to 8-ounce) ramekins and place in a large baking dish. Add boiling water to baking dish until it reaches halfway up ramekins. Carefully place in oven and bake 50 minutes or until centers are just set. Remove from oven and remove ramekins to a wire rack to cool. Chill completely in refrigerator, about 3 hours.