Mix the wet ingredients: In a large bowl, beat the shortening with the brown sugar and granulated sugar until the mixture is smooth and creamy. Add the egg, pumpkin puree, and pumpkin spice, and beat until all ingredients are well incorporated
Add the dry ingredients: In the same bowl, mix in the flour, baking soda, cream of tartar, and salt. Use a spatula or hand whisk to mix until a uniform dough forms.
Chill the dough: Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes.
Form the cookies: Preheat the oven to 350°F (180°C). Using a #20 cookie scoop, form dough balls and place them on a baking sheet lined with parchment paper, leaving space between them.
Bake: Bake the cookies for 13 minutes, until the edges are golden but the center remains soft.
Prepare the cinnamon sugar: While the cookies are baking, mix the 4 tablespoons of granulated sugar with the cinnamon in a small bowl.
Roll the cookies in cinnamon sugar: Once the cookies are out of the oven, let them cool slightly for a few minutes. Then, roll each cookie in the cinnamon sugar mixture.
Cool completely: Let the cookies cool on a rack until they are completely cooled.