Preheat your oven to 350°F (175°C) and prepare an 8x8 inch baking pan with non-stick spray or parchment paper.

Melt the unsalted butter in a microwave-safe bowl for about 30 seconds, and stir in the brown sugar until smooth.

Add one egg and a teaspoon of vanilla extract to the mixture, whisking until well-blended.

Sift together the all-purpose flour, cinnamon, baking powder, and salt in a separate bowl. Gradually add to the wet ingredients and stir gently.

Fold in the freshly shredded carrots until evenly distributed throughout the batter.

Beat softened cream cheese with granulated sugar until smooth, then add an egg yolk and vanilla extract, mixing well.

Spread half of the carrot cake batter into the prepared baking pan.

Spoon half of the cream cheese frosting mixture over the carrot cake batter and spread it out.

Pour the remaining carrot cake batter over the cream cheese layer and dollop the rest of the frosting on top.

Use a knife or skewer to gently swirl the batters together to create a marbled effect.

Bake for 35 to 40 minutes until the edges are golden brown and the center jiggles slightly.

Allow the bars to cool completely in the pan before lifting them out and cutting into squares.