Preheat your oven to 350°F (175°C). Grease an 8×8-inch baking pan or line it with parchment paper and lightly spray with non-stick spray. Set aside.

In a microwave-safe bowl, melt the butter in 30-second intervals. Stir to finish melting if needed. Let it cool slightly before combining with sugar.

In a medium mixing bowl, combine the melted butter and brown sugar. Whisk until smooth and glossy. Stir in the egg and vanilla extract until fully incorporated.

Add in the flour, cinnamon, baking powder, and salt. Mix until just combined, being careful not to overmix. Gently fold in the shredded carrots.

In a separate bowl, beat the cream cheese and granulated sugar until smooth. Add the egg yolk and vanilla extract. Continue beating until creamy and well-blended.

Pour half of the carrot cake batter into the prepared pan. Spread it into an even layer using a spatula. Drop spoonfuls of half the cheesecake mixture across the surface.

Add the rest of the carrot cake batter on top, spreading it around and between the cheesecake dollops. Top with the remaining cheesecake batter in small spoonfuls.

Using a knife or skewer, gently swirl the two batters together. Swirl as much or as little as you like—just enough to create a marbled effect.

Bake for 35–40 minutes, or until the edges are golden and the center is mostly set. There should be very little jiggle in the middle.

Let the bars cool completely in the pan. Once cool, cut into squares and store in an airtight container in the fridge.