In a medium bowl, combine the flour, baking powder, salt, cinnamon, and nutmeg. Whisk to blend and set aside. In the bowl of an electric mixer, beat together the butter and sugars on medium-high speed until light and fluffy, 2-3 minutes. Blend in the pumpkin puree. Beat in the egg and vanilla until incorporated. With the mixer on low speed add in the dry ingredients and mix just until incorporated.

Preheat the oven to 350˚ F. Line baking sheets with silicone baking mats or parchment paper. Combine the sugar and spices for the coating in a bowl and mix to blend. Scoop the dough (about 2½ tablespoons) and roll into a ball. Coat the dough ball in the sugar-spice mixture and place on the prepared baking sheet. Repeat with the remaining dough to fill the sheets, spacing the dough balls 2-3 inches apart, about 10 on a sheet. Dip the bottom of a flat, heavy-bottomed drinking glass in the bowl of unused dough to get it sticky. Then dip the glass in the sugar-spice mixture, and use the bottom to flatten the dough balls to about 1/4-inch thickness, dipping the glass in the sugar mixture before flattening each time.

Bake the cookies for 10-12 minutes, or until just set and baked through. Let cool on the baking sheets about 5 minutes, then transfer to a wire rack to cool completely. Repeat with the remaining dough. Store in an airtight container.