1. Preheat oven to 350°F. Line an 8×8-inch baking pan with heavy-duty aluminum foil, leaving overhang on the sides. Spray the foil lightly with cooking spray.

2. Melt butter in a microwave-safe bowl for about 1 minute, then let cool slightly. Whisk in the egg, brown sugar, salt, and vanilla until smooth. Sift in flour, baking powder, cinnamon, and nutmeg, stirring gently until just combined.

3. Fold freshly grated carrots into the batter until evenly distributed. Pour into your prepared pan and smooth the top with a spatula.

4. Beat softened cream cheese with egg yolk and granulated sugar using an electric mixer on high speed for about 4 minutes until completely smooth and fluffy.

5. Drop spoonfuls of cream cheese mixture over the carrot cake batter. Use a butter knife to swirl the cream cheese through the batter, creating marbled patterns.

6. Bake for 25 to 30 minutes until a toothpick inserted in the center comes out clean. The edges should be lightly golden.

7. Remove from oven and let cool completely in the pan for at least 2 hours. Use the foil overhang to lift the bars out of the pan, then slice into squares with a sharp knife.