Combine mashed sweet potato (about 1 1/4 cups), 1/4 cup brown sugar, and lemon juice; spoon potato mixture into a buttered 10" x 2" quiche dish to form a 1/4" thick layer.
Stir together cream, granulated sugar, egg yolks, and vanilla in a medium saucepan. Cook mixture over medium-low heat, stirring constantly, about 15 minutes or until hot. (Do not boil.)
Pour over sweet potato mixture in prepared dish. Place dish in a shallow pan. Add hot water to pan to a depth of 3/4" (about halfway up dish).
Bake at 325º for 1 hour or until a knife inserted in center comes out almost clean. Carefully remove dish from water. Cool custard on a wire rack. Cover and chill at least 8 hours.
Sprinkle custard with 1/3 cup brown sugar; place dish on a jellyroll pan. Broil 5 1/2" from heat 3 to 5 minutes or until sugar melts. Let stand 5 minutes to allow sugar to harden before serving.
Tip: Removing a hot dish from a hot water bath can be tricky. We recommend wearing insulated rubber gloves to grasp the hot dish--they'll protect your hands from both the hot dish and hot water.