Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

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

In another bowl, cream together the brown sugar, granulated sugar, and softened butter 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 walnuts (if using).

Drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 10-12 minutes, or until the edges are lightly golden. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

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

Gradually add the powdered sugar, mixing until creamy and well combined.

Stir in the vanilla extract until fully incorporated.

Once the cookies are completely cooled, spread a generous amount of frosting on top of each cookie.