Preheat oven to 350 degrees F.
Line baking sheet with parchment paper.
In large bowl combine oats, flour, flax, cinnamon, baking soda, baking powder, and salt. Stir well to combine.
In medium bowl, whisk together honey, coconut oil, milk, egg, and vanilla until well combined.
Pour wet ingredients into the dry ingredients and stir with a spatula until completely mixed.
Mix in shredded carrots.
Make ~3 tablespoon sized cookie balls, and flatten slightly, placing them on prepared baking sheet.
They will not spread much.
Bake in preheated oven for 9-11 minutes.
Let cool for 5 minutes then transfer to cooling rack to cool completely.
Make the frosting by whisking together all frosting ingredients.
Drizzle frosting over cooled cookies.
Eat and enjoy!
Store in airtight container in the refrigerator for 1 week.