Preheat the oven to 350°F (175°C). Grease and flour three 8-inch round cake pans and set aside.
Mix the dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, clove, and black pepper. Set aside.
Blend the wet ingredients: In a large mixing bowl, beat together the brown sugar, vegetable oil, molasses, and applesauce until smooth. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Combine the mixtures: Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Scrape down the sides of the bowl as needed.
Bake the cakes: Evenly divide the batter between the prepared pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool completely before frosting.
Prepare the eggnog buttercream: In a large bowl, cream the butter on medium-high speed until light and fluffy. Gradually add the confectioners’ sugar, mixing on low speed. Add the eggnog, nutmeg, and heavy cream, and beat on high speed for 1-2 minutes until the frosting is fluffy and smooth.
Make the white chocolate ganache: In a small saucepan, bring the heavy cream to a simmer. Pour the hot cream over the white chocolate chips in a heatproof bowl. Stir until the mixture is smooth. Let the ganache cool for 10-20 minutes, until it reaches a thick but pourable consistency.
Assemble the cake: Spread a layer of eggnog buttercream between each cake layer. Frost the top and sides of the cake with the remaining buttercream. Drizzle the white chocolate ganache over the top, letting it drip down the sides.
Optional: Lightly sprinkle the top of the cake with ground cinnamon or nutmeg for a festive touch.