Preheat oven to 300 degrees. In a medium sauce pan, heat the cream and vanilla to a simmer. Remove pan from heat and let sit for 10 minutes. In a bowl whisk together the sugar and yolks until they are a pale yellow. Whisk cream into the egg mixture and pour into 6 custard dishes.
Place dishes in a large baking dish lined with a towel. Pour boiling water into baking dish so that it comes to half way up the custard dishes. Bake for 30 minutes or until custard is firm but still wiggles. Chill for at least one hour. Top with brown sugar in an even layer and place under broiler until sugar melts and bubbles. Serve at room temperature.