Preheat oven to 350 degrees. Spray a donut pan (6-count pan) with nonstick cooking spray and set aside. In a large mixing bowl, whisk together the flour, baking powder, pumpkin pie spice, nutmeg, and salt. In a separate mixing bowl, mix together the brown sugar, pumpkin, milk, egg, butter, and vanilla extract. Mix well. Add the dry ingredients to the wet ingredients, lightly sitrring until just combined.