Begin by lining two cookie sheets with parchment paper and set aside. Preheat oven to 350°F (175°C)
In a large bowl, whisk together the melted butter, granulated sugar, and brown sugar until smooth and glossy. Add the egg and mix until fully combined.
Next, add the flour, baking soda, salt, cinnamon, and nutmeg (yes, in the same bowl is fine!) and mix until just combined. Fold in the rolled oats and shredded carrots until evenly distributed.
Using a standard cookie scoop, portion the dough into balls and place them on a lined baking sheet, leaving space between each cookie. Roll them into balls and ensure they are tight so that it doesn’t crumble and come apart during the baking process.
Bake at 350°F (175°C) for 10–12 minutes, or until the edges are set and the centers still look slightly soft.
As soon as the cookies come out of the oven, place an upside-down drinking glass over each cookie and gently swirl it in a circular motion to create perfectly round, uniform cookies.
Let the cookies cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely before assembling.
In a bowl, beat together the softened cream cheese and butter until smooth and creamy. Add the powdered sugar and mix until combined. Add the milk, 1 teaspoon at a time, until you reach a smooth, spreadable consistency. If the frosting is too thin, add more powdered sugar, 1 tablespoon at a time.
Spread a layer of cream cheese frosting onto the flat side of one cookie using an offset spatula or spoon. Top with another cookie and gently press to form a sandwich.