Preheat oven to 400 degrees F. Coat a donut pan with nonstick spray.
In a large bowl, combine flour, baking powder, pumpkin pie spice, salt and baking soda.
In the bowl of an electric mixer fitted with the paddle attachment, beat 1/2 cup granulated sugar, brown sugar and vegetable oil on medium-high until well combined, about 1-2 minutes. Beat in eggs, one at a time, until well combined. Beat in pumpkin and vanilla until just combined. Gradually add flour mixture to sugar mixture at low speed, beating just until incorporated.
Using a piping bag fitted with a round piping tip or a large Ziplock bag with the corner cut off, pipe the batter evenly into the donut pan. Place into oven and bake for 10-12 minutes, or until donuts are slightly browned and spring back when touched.
In a medium bowl, combine remaining 1/2 cup granulated sugar and cinnamon.
When the donuts are done, cool for 10 minutes and brush the tops with butter, gently tossing in the cinnamon sugar mixture.