First, preheat the oven to 350F then lightly grease the large donut pan with cooking spray.
In a medium bowl, combine the pumpkin puree, olive oil, butter, vanilla, egg, brown sugar, and granulated sugar and whisk until smooth.
1&1/2 cup pumpkin puree, 1/3 cup olive oil, 1/4 cup butter, 1 tsp vanilla extract, 2 egg, 2/3 cup brown sugar, 1/2 cup granulated sugar
Add the flour, pumpkin pie spice, baking powder, and sea salt. Stir the mixture just until combined. Do not overmix.
2 cup AP flour, 2 tsp pumpkin pie spice, 2 tsp baking powder, 1/2 tsp salt
Place the batter in a piping bag or a plastic bag over a cup and transfer the donut mixture to the bag. If using the plastic bag method, snip off one of the corners and "pipe" the batter into the prepared donut pan. This recipe should make 8 large donuts.
Bake for 25 minutes, or until a knife of a toothpick inserted in comes out clean. Let the donuts cool for 10 minutes then transfer to a cooling rack.