Put some vanilla paste with milk in a saucepan and heat the liquid briefly. Add the cream to the milk and heat again briefly while stirring (do not let it boil). Separate eggs. Cream the egg yolks with the sugar for about 2 minutes and add the cream mixture while stirring.
Place fireproof ramekins in a large casserole dish. Pour hot water into the casserole dish so that the ramekins are about two-thirds submerged. Pour the crème brûlée mixture into the ramekins. Place the complete casserole dish in the preheated oven and bake for approx. 40-50 minutes.
After cooling (preferably before serving), sprinkle 3 teaspoons of brown sugar on each dessert and flambé with a flambé burner until the sugar melts and caramelizes.