Preheat Oven: Preheat the oven to 350°F (175°C). Grease a 13×9-inch metal baking pan with nonstick baking spray. Line the pan with parchment paper, leaving an overhang for easy removal later, then lightly grease the parchment paper with nonstick baking spray as well.

Prepare Carrot Puree: Fill a medium pot with 1 inch of water and place a steamer basket inside. Cover the pot and bring the water to a boil over high heat. Add the carrots to the steamer basket and reduce the heat to low. Cover the pot and steam until the carrots are very tender, 20 to 25 minutes. While the carrots are still hot, transfer them to a small bowl with the butter. Using an immersion blender or food processor, puree until smooth and then set aside to cool (you should have about 1 cup of carrot puree).

Prepare Carrot Cake Batter: In a medium bowl, whisk together the flour, baking powder, cinnamon, cardamom, and cloves. Place a large saucepan over medium heat and add 12 tablespoons of the butter (1½ sticks). Let it melt, then continue to cook, swirling the pan occasionally, until the butter is golden brown and has a nutty aroma, 5 to 6 minutes. Remove the pan from the heat and add the remaining 4 tablespoons of butter. Swirl the pan continuously until the butter stops foaming, then whisk in the brown sugar, vanilla, and salt. Transfer to a large bowl and let the mixture cool to room temperature, about 30 minutes.

Prepare Cream Cheese Batter: Add the cream cheese to a medium bowl. If it is not soft enough to whisk, microwave in 10-second intervals until it is softened but not melted. Whisk in the sour cream, granulated sugar, vanilla, and egg until there are no lumps and set aside.

Assemble and Bake: Pour half of the carrot cake batter into the prepared pan and spread it into an even layer. Drop spoonfuls of the cream cheese batter over the carrot cake batter. Use a butter knife to swirl the cream cheese batter into the carrot cake batter. Pour the remaining carrot cake batter over the top and spread it into an even layer. Drop spoonfuls of the remaining cream cheese batter over the top and swirl again. Sprinkle the toasted pecans over the top.

Bake: Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.

Cool and Serve: Let the bars cool completely in the pan on a wire rack. Once cooled, lift the bars out of the pan using the parchment paper overhang and cut into squares.