In a large bowl, whisk together the flour, baking soda, cream of tartar, salt, and spices; set aside. In another large bowl, beat together the butter, oil, pumpkin, sugars, vanilla, and eggs. Mix until smooth. Then, slowly mix in the dry ingredient until completely incorporated.
Using a 1 1/2 tablespoon scoop, place the dough onto a baking sheet lined with parchment paper (or a silicone baking mat). Use a glass to flatten the dough to about 1/2 inch thick. (If the dough sticks, press the bottom of the class in granulated sugar before flattening the dough.) Bake for 8-9 minutes.
Once baked, transfer the cookies to a cutting board to cool.
While the cookies cool, prepare the glaze. Whisk together all of the ingredients until smooth. If your glaze is too thick, add more milk. If it's too thin, add more powdered sugar.
Once the cookies are cool, use a spoon and spread glaze over top of each cookie. Let the glaze harden before serving or packing away.