Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a bowl, mix melted coconut oil, coconut sugar, and vanilla extract until well combined.
Add the egg and oat milk, then mix in shredded carrots.
Add almond flour, cinnamon, nutmeg, baking soda, and salt. Mix until a dough forms.
Use a double cookie scoop to shape dough into balls, then flatten them with the palm of your hand. Bake for 9-12 minutes or until golden brown. Let cool.
Meanwhile, in an electric mixer, whisk softened vegan butter until light and fluffy. Add powdered sugar, vanilla, and oat milk, and whisk until combined.
Transfer frosting to a piping bag and pipe onto cooled cookies. Top with freshly chopped shredded carrots and walnuts. Enjoy!