This makes one large crème brûlée for sharing. Prepare the custard up to a day ahead, and chill the topping for at least one hour. Set out small plates and a large serving spoon so that guests can help themselves.
Preheat oven to 350 degrees. Place 11- by 8-inch (8-cup capacity) shallow ceramic baking dish in roasting pan.
Mix cream and 2/3 cup sugar in medium saucepan. Bring to simmer, stirring until sugar dissolves. Whisk yolks in medium bowl. Gradually whisk in hot cream mixture, then rum, brandy, nutmeg, and salt. Transfer to baking dish. Pour enough hot water into roasting pan to come halfway up sides of dish. Carefully transfer pan to oven.
Bake until custard is set around edges but center still jiggles slightly when dish is gently shaken, about 40 minutes. Remove ceramic dish from water. Chill custard on rack until cold, at least 3 hours. (Can be made 1 day ahead. Cover and keep chilled.)
Preheat broiler. Press brown sugar through strainer over custard to cover completely and evenly. Watching closely, broil custard 4 to 6 inches from heat source until sugar bubbles and caramelizes, about 2 minutes. Chill custard until topping hardens, at least 1 hour and up to 3 hours. Serve cold.