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Step 1
Pre-heat the oven to 350. Butter a cookie sheet or line it with parchment paper.
Step 2
Beat the butter and sugars together until they are fluffy and smooth- this takes about 3 minutes. Add in the eggs, one at a time, continuing to mix until they are just combined. Blend in the vanilla.
Step 3
Using ¾ cup of the oats, make oat flour. Just pulse the oats in the food processor or blender until coarse crumbs are formed.
Step 4
In a large bowl whisk together the oat flour, remaining oats, all purpose flour, baking soda, cinnamon, ginger, nutmeg, salt, and cloves. Using a sturdy wooden spoon stir the dry mixture into the wet mixture. Then fold in the shredded carrots.
Step 5
Drop the dough by the rounded tablespoonful onto the prepared cookie sheet. Do not try to flatten or shape the sticky cookie dough – you want the cream pie sandwiches to be fluffy and this dough has a tendency to spread in a tasty but not-so-pretty way.
Step 6
Bake for 10 minutes and then let the cookies cool slightly before transferring to a wire rack to cool completely.
Step 7
Beat together the butter and cream cheese until smooth. Add in the vanilla. Then beat in the powdered sugar. Add the heavy cream a tablespoon at a time, beating until the frosting is smooth and creamy. Spread a bit onto the flat side of half of the cookies. Sandwich the frosting between another cookie.