01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang for easy removal.
02 - Whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a medium bowl until thoroughly blended.
03 - Whisk brown sugar, granulated sugar, eggs, oil, and vanilla in a large bowl until smooth and well incorporated.
04 - Fold grated carrots, drained pineapple, and nuts into the wet mixture until evenly distributed.
05 - Add dry ingredients to the wet mixture. Stir gently until just combined, being careful not to overmix. Set aside.
06 - Beat cream cheese until smooth in a separate bowl. Add sugar, egg, and vanilla. Blend until creamy and completely lump-free.
07 - Spread two-thirds of the carrot cake batter evenly across the prepared pan. Pour cream cheese mixture over the top. Dollop remaining carrot cake batter over the cream cheese layer.
08 - Use a knife or skewer to gently swirl the batters together, creating a marbled pattern throughout.
09 - Bake for 38-42 minutes until a toothpick inserted in the center comes out mostly clean.
10 - Cool completely in the pan. Refrigerate for 2 hours to facilitate clean slicing. Cut into 16 bars and serve chilled or at room temperature.