Preheat oven to 350 degrees F. Cover baking sheets with parchment paper
In a large bowl with an electric mixer, cream powdered sugar, granulated sugar and butter. Or use a stand mixer with the paddle attachment.
Add in oil and mix until combined.
Add in egg yolk, vanilla and pumpkin puree, mix until combined
Whisk together flour, cream of tartar, salt, baking soda, cinnamon, nutmeg, ginger and cloves.
Add this dry mixture to wet mixture.
Dough will be stick. If it is too sticky to work with refrigerate for 20-30 minutes.
Roll dough (2 Tbsp) into a ball and place on covered cookie sheet, 2 inches apart.
Dip the bottom of a glass into the 1/2 cup sugar (grease or moisten the bottom of the glass to get sugar to stick) and press into each cookie, to about 1/4 inch thick. Dip glass into sugar between each cookie.
Bake cookies for about 10 minutes.
Buttercream
Combine sugar, cinnamon and butter.
Add in milk until a nice spreading consistency is found.
Frost cookies.
Notes
Don’t overmix the dough. Mix just until combined to keep the cookies soft and tender.
Chill if needed. This is a soft dough but still workable. If your dough feels too sticky, a quick 15–20 minute chill makes it easier to scoop and shape.
Use pumpkin purée, not pumpkin pie filling. Pie filling has added sugar and spices and will change the texture.
Bake just until set. The cookies should look slightly soft in the center—they’ll finish setting as they cool.
Cool completely before frosting. Warm cookies will melt the buttercream.
Add extra cinnamon. If you want a stronger cinnamon flavor in the frosting, taste and adjust as you mix.
Make ahead friendly. Cookies and frosting can both be refrigerated or frozen for later.