Preheat oven to 350°F (180°C). Line a pan with parchment or baking mats.
Prepare the spice mixture by combining the cinnamon, nutmeg, cloves, ground ginger, and allspice into a small bowl. (You can also use prepackaged pumpkin spice if you prefer, but I like making my own.)
Soften butter to room temperature (or put in the microwave for until soft but not melted). Cream with the sugars for around two minutes, or until light and fluffy.
Add the vanilla and pumpkin puree and blend until combined.
To a separate bowl, combine flour, baking soda, cream of tarter, salt, and 1 tablespoon of the spice mixture. Stir until combined.
Add dry mixture into wet ingredients. Mix until just combined.
To the remaining spice mixture, add 1/4 cup of sugar and stir until combined.
Take a tablespoon of cookie dough, form into a ball, and roll in the sugar-spice mixture until covered. Place on the prepared baking sheet.
When all the cookies have been rolled in sugar, press down on each one with a glass until they're flattened to a couple centimeters tall.
Bake for 8-10 minutes. Let cool before eating.