Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
In a large bowl, cream together the butter and sugar until light and fluffy. Mix in the egg and vanilla until combined.
In a separate bowl, mix together the flour, cinnamon, baking powder and baking soda.
Slowly mix the dry ingredients into the wet ingredients until fully incorporated. Fold in the carrots and oats.
Using a medium cookie scoop, scoop the dough onto the prepared baking sheet and bake in the preheated oven for 15 minutes. Allow to cool completely on the baking sheet.
Once the cookies are cooled, cream together the "filling" ingredients until smooth and creamy.
Make a sandwich by adding the filling to the center of a cookie and topping it with another cookie.