Line a 9”x9” pan with parchment. Preheat the oven to 350F.
Whisk together flour, baking powder, salt, cinnamon, and nutmeg in a bowl.
Blend together the eggs, sugars, oil, and pineapples in a separate bowl.
Blend the dry ingredients into the wet mixture.
Fold the carrots into the batter.
Pour the batter into the baking pan and bake for 35 minutes.
Beat together all ingredients for the frosting.
Take the cake out of the oven and leave to cool.
Spread frosting on top of the cake and cut into squares.