Preheat your oven to 350°F (175°C) and prepare an 8x8-inch baking pan with non-stick aluminum foil, spraying with cooking spray.

Melt ½ cup of unsalted butter in a microwave-safe bowl until liquefied and cool slightly.

Whisk melted butter with 1 large egg, 1 cup light brown sugar, ¼ teaspoon kosher salt, and 1 teaspoon vanilla extract until well combined.

Sift in 1 cup all-purpose flour, 1 teaspoon baking powder, 1 teaspoon ground cinnamon, and ½ teaspoon ground nutmeg, gently stirring until just combined.

Fold in 1.5 cups freshly grated carrots until evenly incorporated.

Beat together 8 ounces softened cream cheese, 1 large egg yolk, and ¼ cup granulated sugar until smooth.

Pour the carrot cake batter into the prepared pan, spoon dollops of cream cheese mixture on top, and swirl gently with a knife.

Bake for 25-30 minutes, checking for doneness with a toothpick.

Allow the bars to cool at room temperature for at least 2 hours before cutting into squares.