Preheat oven to 350 degrees F. Spray an 8x8 baking pan with non-stick spray or line with parchment paper and lightly spray with nonstick baking spray.

In a medium bowl, combine the melted butter and light brown sugar. Mix to combine, then stir in the large egg and vanilla extract.

Add in the all-purpose flour, ground cinnamon, baking powder, and salt. Stir until completely combined, then fold in the shredded carrots.

In a separate medium bowl, beat the room temperature cream cheese and granulated sugar with a hand mixer until smooth. Add the egg yolk and vanilla extract and beat until creamy.

Spread about half of the carrot cake batter into the prepared pan. Drop dollops of half the cheesecake batter over the carrot cake batter.

Add the remaining carrot cake batter on top and around the cheesecake dollops, then finish by adding the remaining cheesecake batter in dollops on top.

Using a knife or skewer, swirl the batters together as much or as little as you like.

Bake for 35-40 minutes until the edges are golden brown and there is very little jiggle to the center. Cool completely before cutting.