01 - Preheat the 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 blended.
03 - In a large bowl, whisk brown sugar, granulated sugar, eggs, oil, and vanilla until smooth. Fold in grated carrots, drained pineapple, and nuts if using.
04 - Add dry ingredients to wet mixture; stir until just combined. Set batter 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 carrot cake batter into prepared pan. Pour cream cheese mixture evenly over top. Dollop remaining batter over cream cheese layer.
07 - Use knife or skewer to gently swirl batters together for marbled effect. Do not overmix.
08 - Bake for 38-42 minutes, or until toothpick inserted in center comes out mostly clean.
09 - Cool completely in pan. Refrigerate for 2 hours for easier slicing. Cut into 16 bars and serve.