Combine the melted butter and brown sugar in a large mixing bowl. Whisk until smooth. Then, add the egg and vanilla extract, mixing until well incorporated. Gradually stir in the flour, cinnamon, baking powder, and salt. Once fully blended, gently fold in the shredded carrots for that signature carrot cake base.
For the swirl, mix the room-temperature cream cheese, granulated sugar, egg yolk, and vanilla extract until smooth and creamy. A hand mixer works wonders to get rid of lumps, ensuring a perfect cheesecake texture.
Spread half of the carrot cake batter into the baking pan, creating an even layer. Add dollops of the cheesecake mixture on top. Layer with the remaining carrot cake batter and follow with the rest of the cheesecake mixture.
Using a skewer or a knife, gently swirl the cheesecake into the carrot cake batter. This step not only creates a visual masterpiece but also blends the flavors beautifully.
Bake in a preheated oven at 350°F (175°C) for 35-40 minutes. Keep an eye on it until the edges start to turn golden brown. Once done, allow the pan to cool completely before slicing into bars.