Preheat oven to 350 degrees F. Spray an 8x8 baking pan with non-stick spray and set aside. You can also line the pan with parchment paper and lightly spray with nonstick baking spray.

Place the 1/2 cup butter in a microwave-safe bowl. Microwave for 30 seconds. If needed, microwave another 15 seconds to melt the butter completely.

In a medium bowl, add the melted butter and 1 cup light brown sugar. Mix to combine. Stir in the 1 large egg and 1 tablespoon vanilla extract.

Add in the 1 cup all-purpose flour, 1 teaspoon ground cinnamon, 1/4 teaspoon baking powder, and 1/4 teaspoon salt. Stir until completely combined.

Fold in the 1 cup shredded carrots. Set aside.

In a medium bowl, add in the 4 ounces cream cheese and 1/4 cup granulated sugar. Beat with a hand mixer until smooth. Add in the 1 large egg yolk and 3/4 teaspoon vanilla extract. Beat until smooth and creamy.

Add about half of the carrot cake batter into the pan and spread it out. Add half of the cheesecake batter to the carrot cake batter. Don’t swirl yet. Add the remaining carrot cake batter on top of the cheesecake batter and around the cheesecake batter. Add the remaining cheesecake batter in dollops on top. Using a knife or skewer, swirl the batters together.

Bake for about 35-40 minutes until the edges are golden brown. There will be very little jiggle to the center. Cool completely before cutting.

Store in an airtight container in the refrigerator.