Heat oven to 350°F. Grease a 13 x 9-inch baking pan. In medium bowl, combine flour, cinnamon, baking powder, salt, and nutmeg; set aside. In large bowl, whisk together eggs, brown sugar, and oil until well blended, about 1 minute. Stir in carrots, pineapple, and flour mixture until just combined. Spread batter evenly in pan.
Bake until top is set and edges pull away from pan, about 25 minutes. Transfer pan to wire rack and cool completely. Cut into 12 bars.
In small bowl, blend together cream cheese and sugar until creamy. Spoon a dollop of cream-cheese mixture onto each bar, and top with grated carrots, if desired.
