Preheat oven to 350°F and line 2 baking sheets with parchment paper.
In a medium-sized bowl, sift together the flour, baking powder, baking soda, salt, and pumpkin pie spice.
In a large bowl, mix together the pumpkin purée, brown sugar, egg, and vanilla extract. Whisk and stir until completely combined.
Working in batches, stir in the flour. Keep adding and stirring until just combined.
Use a medium ice scoop, or a large spoon, to add about 1½ to 2 tablespoons of the batter onto the parchment paper. Use a spoon to spread the dough to about a 2-inch diameter. Continue with the remaining batter, leaving about 1 inch between each round of batter.
Bake for 15 minutes, switching the baking sheets halfway through.
Remove the baking pans from the oven and let the cookies cool for about 10 minutes. Carefully peel the cookies away from the parchment paper and allow them to cool on racks completely, about another 10 to 15 minutes.