Pumpkin-Chocolate Layer Cake

Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 9-inch round cake pans and line the bottoms with parchment paper. (5 minutes)

In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, cinnamon, salt, and allspice. Set aside. (3 minutes)

In a large bowl, combine the granulated sugar, oil, and applesauce using an electric mixer on low speed. Add the pumpkin puree and vanilla extract. Beat in the eggs, one at a time, mixing well after each addition. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Finish mixing with a rubber spatula to ensure no dry pockets remain. (10 minutes)

Pour the batter evenly into the prepared cake pans. Sprinkle half of the finely chopped semisweet chocolate over the top of each pan. Swirl the chocolate into the batter using a metal spatula for a marbled effect. (5 minutes)

Bake in the preheated oven until a toothpick inserted into the center of each cake comes out clean, 25 to 30 minutes. Let the cakes cool in the pans for 5 minutes before inverting them onto wire racks to cool completely, about 30 minutes. (55 minutes)

While the cakes are cooling, prepare the cream cheese frosting. In a mixing bowl, combine the softened cream cheese, confectioners' sugar, and 1 1/2 teaspoons of vanilla extract. Beat with an electric mixer until smooth and creamy. (5 minutes)

Divide the cream cheese frosting into two bowls, keeping approximately 2/3 in one bowl and 1/3 in the other. Add the cocoa powder and remaining 1 teaspoon vanilla extract to the smaller bowl and beat until well combined. (3 minutes)

In a separate bowl, beat the heavy whipping cream on medium-high speed until stiff peaks form. Gently fold 2/3 of the whipped cream into the larger bowl of vanilla cream cheese frosting and the remaining 1/3 into the chocolate cream cheese frosting. (5 minutes)

Once the cakes are completely cool, level them with a serrated knife if needed. Cut each cake layer in half horizontally, creating four layers. (5 minutes)

Place one cake layer on a serving plate or cake stand. Spread with half of the vanilla cream cheese frosting, reaching about 1/4-inch from the edge. Sprinkle with 1/3 of the remaining chopped semisweet chocolate, gently pressing the chocolate into the frosting. Repeat with the next layer, using the chocolate cream cheese frosting and another 1/3 of the chopped chocolate. Add the third cake layer, spreading with the remaining vanilla cream cheese frosting and the remaining chopped chocolate. Top with the final cake layer. (20 minutes)

To make the chocolate ganache, place the bittersweet chocolate in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until the chocolate is melted, about 5 minutes. Remove from heat and whisk in the powdered sugar and butter until smooth and glossy. (10 minutes)

Pour the warm chocolate ganache over the top of the cake, allowing it to cascade down the sides. Spread evenly using an offset spatula. (5 minutes)

Refrigerate the cake for at least 30 minutes to allow the ganache to set before slicing and serving. (30 minutes)