1In a medium bowl, stir together eggs and sugar until smooth; set aside. In the top of a double boiler over simmering water, heat cream until bubbles start to form at edges. Remove from heat and whisk into egg mixture, a little at a time, until fully incorporated. Return mixture to double boiler and cook, stirring constantly, until mixture thickens enough to coat the back of a metal spoon. Cook 2 minutes more, then remove from heat. Cool completely. Stir in vanilla.
2Preheat oven broiler.
3Pour cooled mixture into a 1 quart, shallow baking dish and place dish in an ice bath, in a larger, ovenproof dish. Sprinkle brown sugar over surface of mixture and place under preheated broiler 1 to 2 minutes, until top is lightly browned and bubbly.