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Preheat oven to 325°F. Line a 9x13 (quarter sheet) pan with parchment paper
Place two or three flower nails in the center of the pan, with the flat side resting flat against the cake pan. Make sure they are a few inches apart.
Spray the flower nails with nonstick baking spray.
In a large bowl, mix together the brown sugar, granulated sugar and oil until combined.
Whisk in the eggs. Stir until the batter is smooth.
Sift in the baking powder, baking soda, salt and half of the flour into the batter. Whisk until just combined.
Whisk in the buttermilk, then sift in the cinnamon, nutmeg, cloves, and the remaining flour.
Mix the batter until no streaks of flour remain.
Once the ingredients are fully combined, fold in the grated carrots.
Pour the batter into the prepared pan, and re-center to flower nails. Make sure they're pressed all the way down against the pan.
Bake for 40-45 minutes, or until a toothpick comes out with a few moist crumbs.
Leave the cake in its pan and place on a wire rack to cool. You can also pop the entire pan into the freezer for 45 minutes to accelerate the cooling process.
While the cake bakes and cools, make the cream cheese frosting.
Beat the butter and cream cheese on a medium speed for 30 seconds with a paddle attachment, until smooth.
Add in the vanilla extract and salt, and beat on low until the ingredients are fully incorporated.
Slowly mix in the powdered sugar on a very low speed, 1 cup at a time. Alternate with small splashes of cream.
If the frosting is too thick, add in additional cream (1 teaspoon at a time). If the frosting is too thin, add in more powdered sugar (quarter of a cup at a time).
Cover the cream cheese frosting with a piece of plastic wrap, to prevent a crust from forming until you're ready to use it.
Allow the cake to cool completed, then remove the flower nails from the cake.
Spread an even layer of cream cheese buttercream buttercream on top of the cake, making swirls with an offset spatula.
Decorate as desired, then use a sharp knife to cut the cake into 30 squares.