Start by preheating your oven to 350°F (175°C). Grease an 8x8 baking pan, then line it with parchment paper. This step makes removing the bars easy after baking.

Melt the butter in a bowl and whisk it with the brown sugar until smooth. Stir in the eggs and vanilla extract. Then, add the flour, cinnamon, baking powder, and salt to form a thick batter. Finally, fold in the shredded carrots. Make sure the carrots are evenly distributed for flavor in every bite.

Using a hand mixer, beat the softened cream cheese with granulated sugar, egg yolk, and vanilla extract until smooth. The mixture should be creamy, lump-free, and easy to swirl later.

Spread half of the carrot cake batter evenly into your prepared baking pan. Drop spoonfuls of the cream cheese mixture over this layer. Follow by dolloping the remaining cake batter, then the rest of the cream cheese mixture.

Using a skewer or knife, swirl the cheesecake mixture through the batter to create beautiful marble patterns. Be gentle to keep the layers distinct for a lovely visual result.

Bake the bars for 35-40 minutes, or until the edges are golden brown and the center is only slightly jiggly. Remove from the oven and cool completely in the pan before slicing.