Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, or line them with parchment paper. If using round pans, also grease and flour the parchment.

In a small saucepan, melt 1/4 cup of butter over medium heat. Continue to cook, swirling occasionally, until the butter turns a golden brown and smells nutty. This should take about 5-8 minutes. Remove from heat and set aside to cool slightly.

In a medium bowl, whisk together the all-purpose flour, baking soda, salt, cinnamon, nutmeg, ginger, and cloves.

In a large bowl, cream together the granulated sugar and brown sugar until well combined.

Add the eggs one at a time, beating well after each addition. Stir in the cooled browned butter and vegetable oil, followed by the vanilla extract. Mix until just combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.

Fold in the grated carrots and chopped nuts (if using).

Divide the batter evenly between the prepared cake pans. Bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.

Let the cakes cool in the pans for 10-15 minutes before inverting them onto a wire rack to cool completely.

In a large bowl, beat the softened cream cheese and butter together until smooth and creamy.

Gradually add the powdered sugar, 1 cup at a time, beating well after each addition. Stir in the vanilla extract.

If the frosting is too thick, add the heavy cream or milk, 1 tablespoon at a time, until it reaches your desired consistency.

Once the cakes are completely cool, place one layer on a serving plate. Spread a generous amount of frosting over the top.

Carefully place the second cake layer on top. Frost the top and sides of the cake with the remaining cream cheese frosting.

Decorate with additional chopped nuts or carrot curls, if desired. Slice and serve.