Preheat the oven to 350°F (175°C) and prepare an 8x8 baking pan by greasing it with non-stick spray and lining with parchment paper for easy removal.
Melt your butter in a microwave-safe bowl, then stir in light brown sugar until you have a creamy mixture.
Mix in the egg and vanilla extract until blended smoothly.
Combine the flour, cinnamon, baking powder, and salt in another bowl, then fold this dry mixture into the wet ingredients.
Fold in the shredded carrots thoroughly for a sweet flavor throughout the batter.
Beat the cream cheese with granulated sugar until creamy; then mix in the egg yolk.
Layer half of the carrot cake batter into the prepared pan, followed by dollops of the creamy cheesecake filling, and then top with remaining carrot cake batter.
Swirl the two batters together using a knife or skewer.
Bake for 35-40 minutes until golden brown edges form and the center jiggles slightly.
Cool completely on a wire rack before cutting into bars.
Notes
Optional: Drizzle with a warm cream cheese glaze for an extra indulgent treat.