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. Fold in the grated carrots, pineapple, and nuts if using.
04 - Add the dry ingredients to the wet mixture; stir until just combined. Set aside.
05 - In a separate bowl, beat cream cheese until smooth. Add sugar, egg, and vanilla; blend until creamy and lump-free.
06 - 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.
07 - Use a knife or skewer to gently swirl the batters together for a marbled effect.
08 - Bake for 38-42 minutes, or until a toothpick inserted in the center comes out mostly clean.
09 - Cool completely in the pan. Chill for 2 hours for easier slicing. Cut into bars and serve.