Place the raspberries in 8 individual ramekins. Beat the egg yolks with 13 tablespoons sugar in a mixer bowl until thick and pale yellow.
Bring the cream and vanilla to a boil in a saucepan over medium heat, stirring constantly. Add to the egg yolk mixture; mix well. Return the mixture to the saucepan. Bring to a boil; reduce heat. Simmer until thickened, stirring constantly. Cool slightly.
Strain the mixture over the raspberries. Chill in the refrigerator. Sprinkle the remaining 2 to 3 tablespoons sugar on top. Broil until the top is golden brown and caramelized. Serve immediately.