Prepare an 8x8 baking pan with nonstick spray and set aside. For easy removal add parchment paper.
Melt the butter in a microwave-safe dish.
In a medium-sized bowl, add the melted butter and brown sugar and mix to combine.
Stir in the egg and vanilla.
Add in the flour, cinnamon, baking powder, and salt and stir again until completely combined.
Fold in the shredded carrots. Set aside.
In a medium-sized bowl, add in the cream cheese, sugar, egg yolk, and vanilla and mix until smooth and creamy.
Pour about half of the carrot cake batter into the pan and spread it out with a spatula.
Then, take half of the cheesecake batter and drop spoonful’s over the carrot cake batter. Drop the remaining carrot cake batter by spoonfuls around the cheesecake batter and then finish with drops of the remaining cheesecake batter. Then, take a knife and swirl around until the two are swirled together.
Bake for about 35-40 minutes, the edges will be golden brown and there will be very little jiggle to the center.
Cool completely before cutting. Store airtight in the refrigerator, they are delicious from the fridge!