Preheat the oven to 350 degrees F. Spray a 9-inch springform pan with cooking spray.
Prepare the cake according to the package directions and bake in the prepared pan until a toothpick inserted in the center comes out clean, about 35 minutes. Let cool for 10 minutes in the pan, release the clasp on the collar and remove the cake to a cooling rack to cool completely, about 1 hour. Cut the cake in half horizontally so you have two 9-inch round cakes. Place the bottom half back in the springform pan and close the clasp on the collar. Wrap the other half in plastic wrap and set aside to use later.
Meanwhile, make the mousse: Add the gelatin to a small bowl. Stir in 1/4 cup warm water and let sit for 5 minutes. Whisk the sugar, egg yolks and 1/2 cup heavy cream in a large heatproof bowl set over a pot of simmering water (do not let the bowl touch the water). Cook, whisking constantly, until pale yellow and thickened, 6 to 8 minutes. Add the gelatin and whisk until completely dissolved. Add 1 cup chocolate chips and whisk until melted. Remove the pan from the heat.
Beat 1 cup heavy cream in a large bowl with an electric mixer on medium speed until stiff peaks form, 2 to 3 minutes. Fold into the chocolate mixture and pour over the top of the cake in the springform pan. Refrigerate until the mousse is set, 2 hours and up to overnight.
Microwave the remaining 1/4 cup heavy cream in a small microwave-safe bowl until hot and bubbling, 1 minute 30 seconds. Place the remaining 3/4 cup chocolate chips in a medium heatproof bowl and pour the hot cream over the top. Let sit for 5 minutes, then stir until smooth. Reserve 1/4 cup of the ganache and pour the rest over the top of the mousse. Smooth out with a silicone spatula and refrigerate until hardened, about 15 minutes. Top with the second cake.
Cut 1 inch off each Twix bar, then cut the 1-inch pieces in half crosswise and set aside. Remove the cake from the pan and place on a cake stand or plate. Re-melt the reserved ganache in 30-second intervals in the microwave if needed (you want it to be thick and spreadable). Spread the backs of the large Twix pieces with 2 tablespoons of the ganache and attach them around the outside of the cake like a fence. Drizzle the remaining 2 tablespoons ganache over the tops of the Twix pieces on the cake. Refrigerate until the ganache is hard and the bars are set, about 15 minutes.
Spread the dulce de leche on top of the cake and arrange the shortbread and remaining Twix pieces in a bulls-eye pattern. Refrigerate until ready to serve.
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