Prepare the Oven and Pan:
Preheat the oven to 350°F (175°C). Grease a 13-by-9-inch metal pan with baking spray, line it with parchment paper, and grease the parchment.
Make the Carrot Puree:
Steam the carrot chunks for 20-25 minutes until tender. Combine the hot carrots and butter in a bowl and puree until smooth. Set aside to cool (aim for about 1 cup of puree).
Prepare the Carrot Cake Batter:
In a bowl, whisk the flour, baking powder, cinnamon, cardamom, and cloves. In a saucepan, melt 12 tablespoons of butter until golden brown, then remove from heat and stir in the remaining butter. Once cooled, add brown sugar, vanilla, and salt, then mix in the carrot puree and eggs.
Make the Cream Cheese Batter:
In another bowl, mix softened cream cheese, sour cream, granulated sugar, vanilla, and egg until smooth.
Combine and Layer:
