Preheat the oven to 350ºF. Line a baking sheet with parchment paper or spray with nonstick cooking spray.
In a large mixing bowl, whisk together the flour, cream of tartar, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, mix the butter and cream cheese together until smooth and creamy. Add the 1/2 cup granulated sugar and powdered sugar, beating until smooth and creamy. Add the vegetable oil, egg, vanilla, and almond extract and mix until fully incorporated.
Gradually mix flour mixture into wet ingredients until dough comes together.
Place remaining 1/4 cup sugar into a small bowl. Roll dough into balls that are a little larger than golf balls. Coat ball in sugar and place on lined baking sheet. Repeat process with more dough until you have 6 or 7 balls spaced at least 2 inches apart. Using the bottom of a glass, flatten each dough ball to about 1/2″ thickness. It’s okay if the cookies form a rim on the edges.
Bake cookies for 8-11 minutes or until tops look dry. They should still be pale in color–no browning. Try not to overbake or you’ll end up with hard, crispy cookies. Remove from the oven and allow to cool on the baking sheet for 3-4 minutes before transferring to a wire rack to cool completely.
Make the Frosting:
In a stand mixer fitted with the paddle attachment, beat the butter, pumpkin, salt, pumpkin pie spice, and vanilla together on high until fully incorporated, about 2 minutes. Gradually add the powdered sugar, a cup at a time, until smooth and fluffy.
Transfer frosting to a pastry big fitted with a large round tip and pipe frosting on top of cooled cookies.* For a smoother surface (as pictured), use an offset spatula to smooth out the top.
Notes
*Frosting can also just be spread onto each cookie with a butterknife or offset spatula.