1. Preheat oven to 300 degrees F (150 degrees C).
2. Beat egg yolks, 4 tablespoons sugar and vanilla in a mixing bowl until thick and creamy.
3. Pour cream into a saucepan and stir over low heat until it almost comes to boil. Remove the cream from heat immediately. Stir cream into the egg yolk mixture; beat until combined.
4. Pour cream mixture into the top of a double boiler. Stir over simmering water until mixture lightly coats the back of a spoon; approximately 3 minutes. Remove mixture from heat immediately and pour into a shallow heat-proof dish.
5. Bake in preheated oven for 30 minutes. Remove from oven and cool to room temperature. Refrigerate for 1 hour, or overnight.
6. Preheat oven to broil.
7. In a small bowl combine remaining 2 tablespoons white sugar and brown sugar. Sift this mixture evenly over custard. Place dish under broiler until sugar melts, about 2 minutes. Watch carefully so as not to burn.
8. Remove from heat and allow to cool. Refrigerate until custard is set again.