01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang for easy removal.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
03 - In a large bowl, whisk brown sugar, granulated sugar, eggs, oil, and vanilla until smooth and incorporated.
04 - Fold grated carrots, drained pineapple, and nuts into wet mixture. Add dry ingredients and stir until just combined.
05 - Beat softened cream cheese until smooth. Blend in sugar, egg, and vanilla extract until creamy and lump-free.
06 - Spread two-thirds of carrot cake batter into prepared pan. Pour cream cheese mixture evenly over top. Dollop remaining batter over cream cheese layer.
07 - Run knife or skewer gently through batters to swirl together, creating marbled pattern. Avoid over-mixing.
08 - Bake for 38 to 42 minutes until toothpick inserted in center comes out mostly clean. Center should be set but slightly moist.
09 - Cool completely in pan. Refrigerate for 2 hours before slicing. Cut into 16 bars and serve chilled or at room temperature.