Preheat the oven to 350 degrees F. Line baking sheets or cookie sheets with parchment paper.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, ginger, cinnamon, and nutmeg.
In another bowl, use a hand mixer to cream together the butter, brown sugar and granulated sugar for about 3 minutes. It won't be light and fluffy like typical cookie dough, see note.
Add the egg, pumpkin purée, and vanilla to the sugar mixture and beat just until they come together. It will look a little funny and curdled, but this is okay. Have no fear.
Add the flour to the pumpkin mixture in two batches, mixing until just combined. Make sure all of the flour is incorporated. The dough will be thicker than cake batter, but not as thick as typical cookie dough.
Use a cookie scoop (about 1 tablespoon size) to stack two balls of dough on top of each other for large cookies, leaving 3 inches in between. (Use one scoop for small cookies.)
Bake 15-18 minutes for large cookies, 12-15 minutes for small cookies, until they are golden around the edges. Allow to cool for 5 minutes on the baking sheet, then gently slide the parchment paper with the cookies onto a rack to cool completely before serving. (The cookies will be too soft when they come out of the oven to move individually to the rack without breaking, so keep them on the parchment.)