In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.

In a large bowl, whisk the melted butter and granulated sugar until smooth. Add the pumpkin puree, egg, and vanilla, and whisk until fully incorporated. The mixture will look slightly curdled at first - keep whisking until it comes together.

Add the dry ingredients to the wet ingredients and stir with a rubber spatula until just combined and no streaks of flour remain. Do not overmix. Cover the bowl and chill the dough for 30 minutes in the refrigerator - this firms it up so you can roll it properly.

Preheat your oven to 350 degrees F. Line two baking sheets with parchment paper. Place the 1/2 cup granulated sugar in one shallow bowl and the 1 cup powdered sugar in another.

Scoop about 1.5 tablespoons of dough and roll into a ball. Roll first in granulated sugar to coat completely, then roll in powdered sugar to coat heavily - this double coating creates the best crackle effect. Place on prepared baking sheets about 2 inches apart.

Bake for 10-12 minutes, until the cookies have puffed, cracked across the tops, and look set around the edges but still slightly soft in the centers. The powdered sugar will have spread into beautiful crackled patterns. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.