01 - Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving some 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 fully incorporated.
04 - Fold in the grated carrots, drained pineapple, and nuts if using until evenly distributed throughout the batter.
05 - Add the dry ingredients to the wet mixture and stir until just combined. Do not overmix. Set aside.
06 - In a separate bowl, beat cream cheese until smooth. Add sugar, egg, and vanilla; blend until creamy and lump-free.
07 - Spread 2/3 of the carrot cake batter into the prepared pan. Pour the cream cheese mixture evenly over the top. Dollop the remaining carrot cake batter over the cream cheese.
08 - Use a knife or skewer to gently swirl the batters together for a marbled effect, being careful not to overmix.
09 - Bake for 38–42 minutes, or until a toothpick inserted in the center comes out mostly clean.
10 - Cool completely in the pan. Chill for 2 hours for easier slicing. Cut into 16 bars and serve.