Special equipment: A multi-opening or spaghetti-style piping tip, such as Ateco 234 (optional): an unlined copper pot, a digital-alarming candy thermometer
Preheat the oven to 350 degrees F. Line a regular-size cupcake or muffin pan with 12 cupcake liners.
In the bowl of an electric stand mixer, cream the butter and sugars together, about 5 minutes. Meanwhile, combine the flours, baking soda, baking powder and salt in a medium bowl. Whisk together and set aside. Combine the eggs and vanilla in a small bowl. Scrape down the sides of the mixer bowl, and then add the vanilla and egg mixture, one egg at a time, with the mixer on low speed. Add the Caramel. Scrape down the sides of the bowl again, and then increase the speed to medium and combine thoroughly. With the mixer the lowest speed, add the flour mixture and the sour cream, alternating between the two, beginning and ending with the flour. Mix only until just combined, do not over-mix.
Fill the cupcake liners with a 16-size ice cream scoop, or about half full, and bake until dark golden and baked through, about 15 minutes. Cool the cupcakes completely.
To assemble: Core each cupcake using an apple corer. Fill each cupcake with the Black Sesame Pastry Cream and generously frost with the Chestnut Cream Frosting so that the frosting resembles a mountain of noodles. Top each cupcake with a pair of the Black and White Sesame Chopsticks.
In a heavy-bottomed saucepan (or preferably an unlined copper pot), combine the sugar with 4 tablespoons water to moisten. Place over medium-high heat and, without stirring, cook until the sugar is dark amber in color. Meanwhile, place the cream in a saucepan over medium heat and warm to a simmer. Turn off the heat on the caramelized sugar and slowly add the warmed cream while stirring the caramel with a wooden spoon. Be careful as the mixture will splatter. Allow to thicken slightly over medium heat, about 5 minutes. Stir in the lemon juice if using. Cool completely.
Bring the milk to a boil in a small saucepan. In a small bowl, whisk together the yolks with the sugar and cornstarch until smooth and well blended. While whisking, slowly pour in one-quarter of the milk into the yolk mixture to temper the yolks. Add the remainder of the milk, while whisking. Pour back into the saucepan and place on medium heat. Whisk vigorously and constantly until the mixture thickens. Remove from the heat and whisk in the vanilla extract. Allow to sit for 5 minutes. Whisk in the butter, piece by piece. Add the tahini and black sesame powder, and whisk to blend. Cool completely.
Cream together the chestnut paste and chestnut puree in a food processor fitted with a metal blade until smooth. Add the softened butter, powdered sugar, rum and vanilla extract, and continue to process until well blended. If chunks remain, press the cream through a fine sieve to remove any large chestnut chunks. Place the cream in a piping bag with a "spaghetti" tip.
Line a half sheet pan with a sheet of parchment paper. Coat the paper with cooking spray. Coat a wide spatula and a rolling pin with cooking spray.
In a small, heavy-bottomed saucepan or unlined copper pot, combine the sugar, vinegar and 1 teaspoon water. Cook over low heat until the sugar is melted and the mixture is thick. Stir a little. Cook until the sugar reaches 248 degrees F on a candy thermometer. At this point, add the sesame seeds to the sugar and stir well with a wooden spoon. Quickly scrape the mixture onto the parchment and spread evenly, first with the prepared spatula and next with the rolling pin. The desired thickness is about 1/16-inch thick. Cool at room temperature for about 10 minutes.
Cut the candy into 12 chopstick shapes, each about 3 inches long, with the aid of a Chinese cleaver and a heavy pan. This technique makes cutting easier, even when the candy gets a bit hard. Let the candy cool completely.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.