Preheat your oven to 350°F (175°C). Grease two 8-inch cake pans and line the bottoms with parchment paper for easy removal.
In a large mixing bowl, whisk together the sifted flour, cinnamon, cloves, baking powder, baking soda, and salt until evenly combined.
In a separate bowl, beat the eggs and sugar until the mixture is smooth, light, and slightly fluffy, about 2-3 minutes.
Pour in the vegetable oil and vanilla extract, then continue to mix until fully incorporated and the mixture looks glossy.
Gradually add the dry ingredients to the wet mixture, folding gently with a spatula or mixing on lowest speed until just combined. Do not overmix.
Fold in the grated carrots carefully to distribute evenly without deflating the batter.
Divide the batter evenly between the prepared pans, smoothing the tops with a spatula for an even bake.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean and the cakes are golden brown.
Remove the cakes from the oven and let them cool in their pans for 10 minutes. Then, transfer to a wire rack to cool completely.
In a mixing bowl, beat the softened cream cheese and butter until creamy and smooth, about 2 minutes.
Gradually add the powdered sugar and vanilla extract, beating on low speed until fully incorporated and the frosting is fluffy.
Spread a generous layer of cream cheese frosting over the first cake layer, top with the second layer, and frost the outside with the remaining frosting.
Slice and serve the cake, enjoying the moist crumb and tangy frosting as the aroma of spices fills the air.
