Start by setting your oven to 350°F (175°C) so it’s ready when you are. Take a 9×13-inch sheet pan, grease it lightly with butter or oil, then line it with parchment paper. This makes it easier to lift the cake out later.

Peel your carrots and grate them finely use the smaller holes on a box grater. You’ll need 2½ cups, which is about 400 grams. Set the grated carrots aside for now.

In a large mixing bowl, combine the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves. Whisk everything together so it’s evenly mixed. This ensures the spices and leavening agents are distributed throughout the batter.

In another large bowl, beat the granulated sugar, brown sugar, and eggs together until the mixture becomes light and fluffy. This takes about 2 minutes with a hand mixer or stand mixer. Add the oil and buttermilk, and mix again until the liquid is smooth and fully combined.

Fold the grated carrots into the wet mixture using a spatula or wooden spoon. Once that’s mixed in, slowly add the dry ingredients. Stir just until you no longer see streaks of flour—be careful not to overmix, or the cake can turn out dense.

Pour the finished batter into your prepared pan and spread it out evenly. Put it in the oven and bake for 40 to 45 minutes. To check if it’s done, insert a toothpick into the center if it comes out clean or with just a few crumbs, the cake is ready. Let it cool in the pan for 15 minutes, then carefully lift it out and place it on a wire rack to cool completely.

In a clean bowl, beat the room-temperature butter until it’s smooth. Add the cold cream cheese (this helps keep the frosting thick) and beat until just combined it should still hold its shape. Mix in the lemon juice and vanilla extract. Gradually add powdered sugar while beating until the frosting becomes light and fluffy.

Once the cake is completely cool, spread the cream cheese frosting over the top using a spatula or offset knife. Try to make it as smooth as possible. Cut into squares and serve.