Make One-Bowl Chocolate Cake Batter and bake following the cupcake instructions.
Make the chocolate curls: Coat a mini loaf pan or other small dish with cooking spray. (If using a larger dish, you will need more white and semisweet chocolate.) Melt the white chocolate in the microwave in 30-second intervals, stirring, until smooth, then pour into the prepared pan. Refrigerate until just beginning to set, about 5 minutes. Melt the semisweet chocolate in the microwave in 30-second intervals, stirring, until smooth, then pour over the white chocolate. Refrigerate until both layers are firm, about 30 minutes. Remove the layered chocolate from the dish and let sit at room temperature, 10 minutes. Using a vegetable peeler, shave from the side to create brown-and-white curls.
Make the frosting: Beat the cream cheese, butter and salt in a large bowl with a mixer on medium-high speed until fluffy, about 2 minutes. Reduce the speed to medium low and gradually beat in the confectioners' sugar until smooth, then beat in the vanilla. Increase the speed to medium high and beat until thick and fluffy, about 2 minutes.
Spread or pipe the frosting on the cupcakes and top with the chocolate curls.