Pre-heat the oven to 375° F.
Cream or mix together the butter, cane sugar, and light brown sugar.
Then mix both the egg and vanilla extract into the creamed mixture.
Next add in the pumpkin, and mix everything together well.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, salt, and pumpkin pie spice.
Stir the dry ingredients into the creamed mixture, and mix really well, being sure to scrape the sides of your bowl.
Using a cookie scoop, scoop 1-inch balls of dough onto an ungreased cookie sheet.
Press each cookie with the bottom of a glass coated in cane sugar. If you want to frost the cookies, you can omit the sugar.
Bake at 375° F for about 12 minutes, or until the edges of the cookies begin to turn a nice golden brown.
Remove the baked cookies from the cookie sheet, and place them on a wire rack to cool. If you want to frost the cookies, just spread your favorite frosting on the top of each cooled cookie.