Preheat the oven to 350?F (175?C).

In a mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.

In another bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Beat in the egg and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the grated carrots and chopped walnuts (if using).

Using a cookie scoop, drop rounded tablespoons of dough onto a baking sheet lined with parchment paper.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.

Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

In a mixing bowl, beat together the softened cream cheese and butter until smooth.

Gradually add the powdered sugar and vanilla extract, mixing until creamy.

Once the cookies have cooled completely, spread a layer of frosting on top of each cookie.

Serve and enjoy your delicious carrot cake cookies!