Preheat the oven to 350 degrees Fahrenheit. Line your baking sheets with the parchment paper.
Mix the cookie ingredients.
To make carrot puree just steam some carrots and then puree them using a blender or mash them up really well.
Mix the flour, baking powder, baking soda, cinnamon, and salt in a bowl. Beat the sugar and butter in your stand mixer. After beating for 2 minutes add in the eggs, one at a time. Then add in the carrot puree and the vanilla extract. Beat the entire mixture until it's smooth. Then stir in the flour mixture until everything is combined well.
Bake the carrot cake cookies.
Use the cookie scoop or a tablespoon to drop the cookies onto the lined baking pans. You should have about 36 cookies from the mixture. You'll have 18 total cookies when you're done because each finished cookie sandwich needs 2 cookies - one for the top and one for the bottom.
Bake the cookies for 13-15 minutes. Let them cool on the baking pans for 5 minutes then move them to wire cooling racks to finish cooling completely.
Mix the frosting ingredients.
Beat the cream cheese, butter, vanilla extract, and cinnamon in your mixer until it's fluffy then gradually beat in the powdered sugar.
Make Cookie Sandwiches.
Spread about a tablespoon of frosting onto the flat side of one of the carrot cake cookies. Then top it with another cookie to make a sandwich. Repeat until all of your cookies are done.