01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - In a large bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy using an electric mixer.
03 - Beat in eggs one at a time, then add vanilla extract, mixing until fully combined.
04 - In a separate bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well blended.
05 - Gradually add dry ingredients to wet mixture, mixing just until combined. Do not overmix.
06 - Fold in grated carrots and chopped nuts (if using) until evenly distributed throughout the dough.
07 - Scoop 3-tablespoon-sized mounds of dough onto prepared baking sheets, spacing at least 2 inches apart to allow for spreading.
08 - Bake for 12 to 14 minutes, or until edges are golden brown and centers are set. Cool on baking sheet for 5 minutes, then transfer to wire rack to cool completely.
09 - Beat cream cheese and butter until smooth and creamy. Gradually add powdered sugar, followed by vanilla and salt, beating until fluffy and well combined.
10 - Once cookies are completely cool, generously frost each with cream cheese frosting. Garnish with additional chopped nuts if desired.