Preheat oven to 350 degrees. Line baking sheets with parchment paper.
Add butter and both sugars to a stand mixer fitted with the paddle attachment. Cream until lighter in color and fluffy, 2-3 minutes.
Add in the egg and vanilla making sure to scrape the sides of the bowl.
Meanwhile in a small bowl combine oats, flour, baking soda, salt, cinnamon and nutmeg.
Slowly add the dry ingredients to the stand mixer and mix just until combined.
Fold in the shredded carrots and nuts by hand.
Portion out cookies onto the prepared baking sheet in heaping tablespoons. Lightly press down on the cookies. Bake for 11-12 minutes or until the edges of the cookies look set. They will still be a bit underdone and that is ok. The cookies will continue to cook as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes then remove them to a cooling rack to cool completely.
Once cookies are cool frost the cookies by either drizzling on the cream cheese frosting or by pipping or spreading on the frosting with a spatula.
Cream Cheese Frosting
Add butter and cream cheese to a stand mixer fitted with the paddle attachment. Cream for 2-3 minutes or until smooth and lump free. Add in vanilla and powdered sugar and mix until smooth.
Notes
For the cream cheese frosting: Use the full recipe is spreading / frosting the cookies. If drizzling the cookies (like I did in the picture cut the recipe in half).