Preheat oven to 350°F (175°C). Grease and line a 9×9-inch baking pan with parchment paper.
In a bowl, whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In another bowl, mix grated carrots, brown sugar, granulated sugar, oil, eggs, and vanilla.
Gradually stir dry ingredients into wet ingredients until just combined. Pour batter into prepared pan.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Cool completely.
Beat cream cheese and butter until smooth. Add powdered sugar and vanilla; beat until creamy.
Spread frosting over cooled bars, add toppings then chill for 20-30 minutes. Slice into squares and serve.