Preheat the oven to 350° F. Line 2 rimmed baking sheets with parchment paper and set aside.
Whisk together the flour, baking powder, baking soda, pumpkin pie spice, cinnamon, nutmeg, and salt. Set aside.
In a small bowl, whisk together the cornstarch and water. Set aside.
In the bowl of an electric stand mixer, beat the butter, cane sugar, and coconut sugar until well blended. Add the pumpkin purée, vanilla extract, and cornstarch slurry. Beat until smooth. (If it separates a bit, it's fine, it will come back together when you add the rest of the ingredients.)
Gently add in the flour mixture, a little bit at a time, until well combined. Be sure to have your mixer on a slow speed when first adding the flour. Once it is somewhat incorporated, you can raise the speed.
Scoop about 2 tablespoons of the dough and roll it into a ball using your clean hands. Place it on the prepared baking sheet. Continue with the remaining dough, spacing them out 2 inches apart.
Gently flatten the balls of dough with your palm or fingers. Slightly damp hands can help if the dough is sticking.
Bake 12 to 14 minutes until the dough has puffed up and is fairly firm.
Let cool on the baking pan for 1 to 2 minutes and then transfer to a wire cooling rack to cool completely, about 20 minutes.