Preheat oven to 350° F. Prepare baking pans with parchment paper or silicone baking mats.
In a bowl, combine flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Whisk to combine and set aside.
In a large mixing bowl, add butter, granulated sugar, and brown sugar. Cream on medium speed using an electric hand mixer.
Add in egg and vanilla extract and continue to mix until smooth.
Add in half of the flour mixture and mix on low speed until just combined.
Pour in milk and continue to mix until smooth.
Add in finely grated carrots and remaining flour mixture and continue to mix on low until the ingredients are fully incorporated. Scrape the sides and the bottom of the bowl to ensure the ingredients are well mixed.
Use a medium (2 tbsp) cookie scoop or spoon to portion the batter onto the baking trays. Allow space between the cookies to allow for spreading.
Bake for 12 minutes until the cookies are puffed up and set.
Remove from the oven and allow the cookies to cool on the pan for a few minutes.
Transfer the cookies to a wire baking rack to cool completely.