01 - Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving 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 well blended.
04 - Gently fold in the grated carrots, drained pineapple, and nuts if using until evenly distributed.
05 - Add the dry ingredients to the wet mixture. Stir until just combined, being careful not to overmix. Set aside.
06 - In a separate bowl, beat cream cheese until smooth and creamy. Add sugar, egg, and vanilla; blend until completely smooth and lump-free.
07 - Spread 2/3 of the carrot cake batter into the prepared pan, creating an even layer. Pour the cream cheese mixture evenly over the top. Dollop the remaining carrot cake batter over the cream cheese layer.
08 - Use a knife or skewer to gently swirl the batters together in a circular or zigzag motion, creating a marbled effect without over-mixing.
09 - Bake for 38-42 minutes, or until a toothpick inserted in the center comes out mostly clean with a few moist crumbs.
10 - Cool completely in the pan. Refrigerate for at least 2 hours for easier slicing. Cut into 16 bars and serve chilled or at room temperature.