Preheat the oven to 350F and lightly grease the large donut pan with cooking spray.

In a medium bowl, combine the pumpkin puree, olive oil, butter, vanilla, eggs, brown sugar, and granulated sugar. Whisk until smooth.

Add the flour, pumpkin pie spice, baking powder, and salt. Stir the mixture just until combined; do not overmix.

Place the batter in a piping bag or a plastic bag over a cup and transfer the donut mixture to the bag. Snip off one of the corners and pipe the batter into the prepared donut pan.

Bake for 25 minutes, or until a knife or toothpick inserted comes out clean. Let the donuts cool for 10 minutes, then transfer to a cooling rack.

For the coating, stir the sugar and cinnamon together in a shallow container.

When the donuts are completely cool, melt the butter and brush each donut with the melted butter. Dip the donuts one by one in the cinnamon sugar to coat them.