Preheat your oven to 350°F (175°C) and spray an 8x8 baking pan with non-stick spray.
In a medium bowl, combine melted butter and light brown sugar. Stir until well mixed.
Add the egg and vanilla extract, blending until smooth.
Fold in the all-purpose flour, cinnamon, baking powder, and salt until just combined. Then, gently fold in the shredded carrots.
In another bowl, beat the cream cheese with granulated sugar until smooth. Add the egg yolk and vanilla, mixing until creamy.
Pour half of the carrot cake batter into the prepared pan and spread evenly. Add dollops of the cream cheese mixture, then top with the remaining carrot cake batter.
Use a knife to swirl the two mixtures together gently.
Bake for 35-40 minutes, or until the edges are golden brown and the center is set with a slight jiggle.
Allow the bars to cool completely in the pan before cutting into squares.
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Notes
Store in an airtight container in the refrigerator for up to a week.