In a medium bowl, stir together eggs and sugar until smooth; set aside.
Heat cream in a double boiler 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.
Pour cooled mixture into a 1 litre, shallow baking dish and place dish in an ice bath, in a larger, ovenproof dish.
Sprinkle dark brown soft sugar over surface of mixture and place under preheated grill for 1 to 2 minutes, until top is lightly browned and bubbly.