Let’s break down the process into easy-to-follow steps.

Step 1: Prepare Oven and Pan. Preheat the oven to 350°F, with the rack in the center of the oven. Grease a metal 13-by-9-inch pan with nonstick baking spray. Line the pan with a piece of parchment paper, being sure to leave an overhang for easy removal later, then lightly grease the parchment paper with nonstick baking spray as well.

Step 2: Make 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 2 tablespoons of 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).

Step 3: Make Carrot Cake Batter (Brown Butter). 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 (1 ½ sticks) of the butter. 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.

Step 4: Finish Carrot Cake Batter. 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.

Step 5: Make 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.

Step 6: Finish Carrot Cake Batter. Once the brown butter-sugar mixture is cool, whisk in the carrot puree until you have a smooth mixture. Add the eggs and yolks all at once and whisk together until fully combined. Add the dry ingredients and stir until just combined, then add the pecans, gently folding them into the batter.

Step 7: Assemble Layers. Spread half of the carrot cake batter into the prepared pan. Using half of the cream cheese mixture, dollop tablespoonfuls on top of the carrot cake batter and swirl it through with a butter knife or wooden skewer.

Step 8: Finish Assembly. Gently spread the remaining carrot cake batter over the top using an offset spatula, aiming to cover most of the cream cheese (it does not have to be perfect). Dollop the remaining cream cheese mixture over the top and repeat the swirling process. Don’t be afraid to really go for it so that you evenly distribute the cream cheese mixture and there’s some in every bite!

Step 9: Bake. Bake until the cream cheese swirl has set and a toothpick inserted into the center of the bars comes out with only a few crumbs attached, 30 to 35 minutes.

Step 10: Cool and Cut. Remove from the oven and transfer to a wire rack to cool completely. Use the parchment paper overhang to lift the cake out of the pan and cut into bars. Serve immediately or store in the fridge until ready to serve.

These instructions are detailed, and clear.