Preheat oven to 400°. Line cookie sheets with parchment paper or silicone mats.
In a food processor or blender, process the oats until finely ground. In a large bowl, combine the ground oats, all-purpose flour, whole wheat flour, cinnamon, baking soda, cream of tartar and salt and set aside.
In another large bowl, beat the butter and shortening together for about 2 minutes with an electric mixer. Add sugar and beat for another minute. Add eggs and vanilla and beat for 2-3 more minutes.
Add the dry ingredients to the butter mixture and mix just until combined. Use a cookie scoop to scoop out the dough and place on prepared cookie sheets, about 2 inches apart. Bake for 8-9 minutes and cool for a couple minutes on cookie sheets before transferring the cookies to a wire rack to cool completely.