Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, mix together the flour, baking powder, salt, cream of tartar, and 2 1/2 tsp of pumpkin pie spice.
In a large mixing bowl, beat the softened butter and sugar until light and fluffy (About 2-3 minutes).
Add the pumpkin puree, egg, and vanilla extract. Mix until well combined.
Gradually add the dry ingredients to the wet mixture, mixing just until combined. Do not overmix.
Cover the dough and refrigerate for at least 30 minutes. This helps the dough firm up, making it easier to roll.
In a small bowl, combine the sugar, and 1 1/2 tsp pumpkin pie spice for the coating.
Scoop out 1 to 1.5 tablespoon-sized portions of dough and roll them into balls. Roll each ball in the sugar-spice mixture to coat thoroughly.
Place the coated dough balls onto the prepared baking sheets, spacing them about 2 inches apart.
Slightly flatten each ball with your hand.
Bake for 10-12 minutes, or until the edges are set and the tops begin to crack. The centers should still be soft.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.