• In a large mixing bowl, combine the butter, oil, pumpkin, sugars, and vanilla. Beat until smooth. Add the egg and yolk, then mix until combined.
• In a separate large mixing bowl, whisk together the flour, baking soda, cream of tartar, salt, pumpkin pie spice, and cinnamon. Gradually mix the dry ingredients into the wet ingredients until combined. Cover the bowl with plastic wrap and chill in the refrigerator for 1 hour.
• Preheat the oven to 350 degrees Fahrenheit (180 degrees Celsius). Line a baking sheet with parchment paper or a baking mat; set aside.
• Scoop and roll the dough into 3.5-inch balls (a #20 scoop is perfect). Place them on the prepared baking sheet. Flatten the dough with the bottom of a glass, jar, or measuring cup to ½-inch thickness.
• Place the cookies in the oven and bake for 10–14 minutes. The edges should be firm, and the middles should be set. Remove from the oven and allow to cool for 5 minutes before transferring to a wire rack to cool completely.

To Make the Cream Cheese Frosting

• Meanwhile, to prepare the cream cheese frosting, using the paddle attachment, cream the butter, vanilla, and salt for 2 minutes or until light and fluffy. With the mixing speed on low, gradually add the powdered sugar and beat until it forms a thick paste. Add the cream cheese and a splash of milk, then mix on the lowest speed possible for 1½ minutes, then STOP!
• Frost the cookies and enjoy immediately. Dust the tops with cinnamon, if desired. Store leftovers in the refrigerator and serve cold or at room temperature.