For the cake: Line a 10-inch springform pan with a circle of parchment paper and spray with nonstick cooking spray. Preheat the oven and follow the box instructions for preparing cake. Pour the batter in the pan. Bake until a toothpick inserted in the center of the cake comes out dry, about 35 minutes. Set aside and let cool while you make the filling. Reduce the oven temperature to 325 degrees F.
For the filling: Meanwhile, mix the cream cheese, granulated sugar, sour cream and cornstarch in a stand mixer fitted with the paddle attachment on medium-low speed until well blended, about 2 minutes. Turn to low speed, then add the eggs one at a time, scraping down the sides of the bowl as needed. Turn to medium and mix until well blended, then add the peppermint and vanilla extracts and mix until incorporated, about another minute. Set aside.
Bring a kettle of water to a boil. Remove the collar of the springform pan and trim the domed top off the cake using a serrated knife. Crumble and reserve the scraps for later use. Lock the collar back in place and wrap the bottom of the springform pan in aluminum foil to prevent water from seeping in during baking. Using a spoon, gently break up the top half of the cake into small-to-medium pieces right in the pan. Pour the filling over the cake pieces in the pan. Using a spoon, slowly mix the cake pieces into the filling for a marbled look.
Place the springform pan in a roasting pan; transfer to the oven. Pour enough boiling water into the roasting pan to come halfway up the sides of the springform pan. Bake until the cake is pale yellow and jiggles slightly in the center, about 1 hour 10 minutes. Let cool in the oven with the door open for 1 hour. Cover and refrigerate overnight.
Remove the collar from the springform pan, using a hot wet towel to warm the sides up to help release the cake if necessary. Return the cake to the refrigerator while you make your frosting.
For the cream cheese frosting: Beat the cream cheese and butter together in a large bowl with an electric mixer on high speed until smooth and creamy. Add the vanilla, salt and 3 cups confectioners' sugar, and beat on low speed for 30 seconds, then switch to high speed and beat for 2 minutes. If you want the frosting a little thicker, add the extra 1/4 cup confectioners' sugar. Transfer to a piping bag fitted with a large star tip.
Pipe the frosting on top of the cake, then drizzle with chocolate sauce and decorate with chocolates, Christmas candies and the reserved crumbled cake.