Preheat your oven to 350°F (175°C) and generously grease two 9-inch round cake pans with cooking spray. In a large mixing bowl, whisk together light or dark brown sugar, granulated sugar, neutral oil, large eggs, and pure vanilla extract until smooth and well combined. Gently fold in all-purpose flour, baking powder, baking soda, ground cinnamon, ground ginger, ground nutmeg, kosher salt, and freshly grated carrots until just incorporated, ensuring not to overmix.

Divide the cake batter evenly between the prepared pans, smoothing the tops with a spatula for an even surface. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Once baked, remove the pans from the oven and let them cool for 10 minutes. Carefully transfer the cakes to a wire rack to cool completely before frosting.

Once your Bunny Cake layers are cool, level the tops if required using a serrated knife for a flat surface. To create bunny ears, take one of the cooled cakes and cut it creatively into two large triangular shapes. Arrange the cake layers and ears on a serving platter.

In a large mixing bowl, beat softened unsalted butter until creamy and light in texture. Gradually add in confectioners' sugar, heavy cream, pure vanilla extract, and a pinch of salt, mixing until fluffy and spreadable. Apply a crumb coat on the entire cake and chill it in the refrigerator for 30 minutes.

Once chilled, remove the Bunny Cake from the refrigerator and generously cover it with the prepared frosting using a spatula. Carefully press sweetened shredded coconut onto the frosting to create the delightful “fur” look. Use jelly beans to form the bunny's eyes, nose, and mouth, completing the whimsical appearance of your Bunny Cake.

Your Bunny Cake is now beautifully decorated and ready to be the star of the table! Display it as a centerpiece at your event, and slice it up to serve immediately.