Preheat oven to 350℉/180℃. Line an 8x8 inch baking pan with parchment paper for easy removal. Set aside.
In a medium sized bowl, add the melted butter and brown sugar and whisk to combine.
1/2 cup butter, 3/4 cups light brown sugar
Add in the egg and vanilla and continue whisking.
1 egg, 1 tbsp vanilla
Add in the flour, cinnamon, baking powder and salt and using a spatula, fold it in again until no dry streaks appear.
1 cup all-purpose flour, 1 1/2 tsp cinnamon, 1/4 tsp baking powder, 1/4 tsp salt
Toss in the shredded carrots and fold in just a few times (don't overmix!)
1 cup shredded carrots
In another medium sized bowl, add in the cream cheese, sugar, egg yolk, flour, and vanilla. Using a handheld electric mixer, mix on medium speed until smooth and creamy.
4 ounces cream cheese, 1/4 cup white sugar, 1 egg yolk, 1 tbsp flour, 1 tsp vanilla
Spread about half of the carrot cake batter into the bottom of the pan with a spatula.
Drop spoonful’s of the cheesecake batter over the carrot cake batter. Then drop the remaining carrot cake batter around the cheesecake batter. Take a knife and swirl around until the two are swirled together.
Bake the bars for 35-40 minutes. The edges will be set, while the middle remains jiggly. The bars will continue to bake as they cool and set.
Cool completely before cutting. Since there is cream cheese in this recipe, I suggest keeping them stored airtight in the refrigerator. Enjoy!