Preheat your oven to 350°F (180°C) and adjust the oven rack to the middle position. Prepare three 8 or 9-inch round pans by spraying them with nonstick cooking spray or lightly greasing them with oil. Line the bottoms with parchment paper, then spray or grease the parchment and dust with flour, tapping out any excess.

In a large bowl, combine the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves (if using) and whisk them together. Set this mixture aside.

Using a food processor with a shredding disk or a box grater, shred the peeled carrots until you have about 3 cups. Set the shredded carrots aside.

In the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl with a hand mixer), beat the eggs along with the granulated and brown sugars on medium-high speed until well combined, which should take about 45 seconds.

Reduce the mixer speed to medium and slowly add the oil in a steady stream, pouring it against the side of the bowl. If the oil splatters, lower the speed until it is fully incorporated, then increase the speed back to high. Mix until the mixture is light in color and well emulsified, about 45 seconds to 1 minute.

Turn off the mixer and gently fold in the flour mixture using a rubber spatula until just combined and no flour streaks remain. Then, stir in the shredded carrots and give the batter a final mix to ensure everything is well combined.

Divide the batter evenly among the prepared pans and smooth the tops. Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean or with a few crumbs attached. Rotate the pans halfway through baking.

Once baked, let the cakes cool in the pans for 10 minutes. Run a small knife around the edges, then carefully flip them out onto a wire rack. Remove the parchment paper, flip the cakes right side up, and allow them to cool completely for 1 ½ to 2 hours before frosting.

While the cakes are cooling, prepare the frosting. In the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl with a hand mixer), beat the softened butter on medium-high speed until creamy and lightened, about 1 to 2 minutes.

Add the confectioners' sugar, salt, and vanilla extract, and continue to beat until the mixture is light and fluffy, which should take about 4 to 6 minutes.

Incorporate the sour cream, then with the mixer on medium speed, add the cream cheese one piece at a time, mixing well after each addition to avoid lumps. Continue until all the cream cheese is fully incorporated.

Increase the mixer speed to medium-high and beat until the frosting is light, fluffy, and smooth, with almost no lumps remaining, about 4 to 6 minutes.

To assemble the cake, place one layer on a cake platter and spread 1 cup of frosting over the top. Add a second layer and press down gently, then spread another cup of frosting on top. Place the final layer on top, pressing lightly, and frost the top and sides of the cake with the remaining frosting. Serve immediately or store under a cake dome or in an airtight container to keep it fresh.