Preheat oven to 300 degrees F (150 degrees C).
Beat egg yolks, 4 tablespoons white sugar and vanilla extract in a mixing bowl until thick and creamy.
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.
Pour cream mixture into the top pan of a double boiler. Stir over simmering water until mixture lightly coats the back of a spoon, about 3 minutes. Remove mixture from heat immediately and pour into a shallow heat-proof dish.
Bake in preheated oven for 30 minutes.Remove from oven and cool to room temperature.Refrigerate for at least 1 hour or overnight.
Preheat oven to broil.
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.
Remove from heat and allow to cool.Refrigerate until custard is set again.
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