Step 1: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line them with parchment paper circles. This ensures your cake doesn't stick.
Step 2: In a large bowl, whisk together the all-purpose flour, baking soda, salt, ground cinnamon, ground nutmeg, and ground cloves until well combined. Set aside.
Step 3: In a separate, even larger bowl, combine the granulated sugar, light brown sugar, eggs, vegetable oil, and vanilla extract. Whisk vigorously until the mixture is well combined and slightly lightened in color.
Step 4: Gradually add the dry ingredients to the wet ingredients, mixing on low speed with an electric mixer or by hand with a spatula until just combined. Be careful not to overmix.
Step 5: Gently fold in the finely grated carrots until they are evenly distributed throughout the batter. If desired, fold in chopped nuts or well-drained crushed pineapple at this stage.
Step 6: Divide the batter evenly between the two prepared cake pans. Bake for 30-40 minutes, or until a wooden skewer or toothpick inserted into the center of the cakes comes out clean. Bake times may vary.
Step 7: Allow the cakes to cool in their pans on a wire rack for 10-15 minutes before inverting them onto the wire rack to cool completely. This is crucial before frosting.
Step 8: While the cakes are cooling, prepare the frosting. In a large bowl, beat the softened cream cheese and softened unsalted butter together with an electric mixer until smooth and creamy, with no lumps.
Step 9: Gradually add the sifted powdered sugar, one cup at a time, beating on low speed until combined, then increasing to medium-high until light and fluffy. Beat in the vanilla extract. If the frosting seems too thick, add a tablespoon or two of milk or cream until it reaches your desired spreading consistency.
Step 10: Once the cake layers are completely cool, place one layer on a serving plate or cake stand. Spread about one-third of the cream cheese frosting evenly over the top. Carefully place the second cake layer on top and spread the remaining frosting over the top and sides of the cake. Garnish with additional grated carrots, chopped nuts, or cinnamon if desired.