• Preheat oven to 350 degrees (F). Cut out three 9-inch round segments of parchment paper to line your cake pans with. Spray each pan generously - sides and bottom - with nonstick cooking spray, then place the parchment paper cut out in the bottom of the pans and spray again. It's important to make sure every bit of pan and paper are sprayed so your cakes don't get stuck. Set pans aside.
• In a large bowl combine the eggs, granulated sugar, light brown sugar, oil, applesauce, sour cream, vanilla, and spices; beat well to combine. Add the flour, baking powder, baking soda, and salt to the wet mixture; stir until just combined. Batter will be on the thicker side but resist the urge to over mix! Add in the carrots and using a rubber spatula gently fold together until incorporated.
• Divide the batter evenly among the prepared pans, smoothing the top with a spatula. Bake cakes for 35 to 40 minutes, or until the top is golden brown and set, and a toothpick inserted in the center of the cake comes out clean. Allow the cake to cool for 20 minutes in the pan, then transfer it to a wire rack to cool completely.
• While the cake is cooling, make your frosting!

For the Cream Cheese Frosting:

• In the bowl of a stand-mixer fitted with the paddle attachment, or in a large bowl using an electric handheld mixer, beat the cream cheese, butter, and vanilla on medium-high speed until completely smooth; about 2 minutes.
• Reduce the speed to low and gradually add the sifted confectioners' sugar. Once all of the sugar has been added beat on high-speed for 1-2 minutes.
• Once the cakes have completely cooled, place one round on a cake stand or large plate; spread the top and sides evenly with frosting. Place the second cake layer on top of the frosted one and press down very lightly to seal them together. Repeat with the final cake layer, then continue frosting the cake, using a thin spatula, offset spatula, or whatever you have that works best, until the top and sides of the cake are evenly frosted.
• Decorate with additional nuts, if desired, then slice and serve! Store this cake in the fridge, covered, for up to 3 days. Bring to room temperature before serving.