First, preheat the oven to 350F then lightly grease the donuts 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.
Add the flour, pumpkin pie spice, baking powder, and sea 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. If using the plastic bag method, snip off one of the corners and "pipe" the batter into the prepared donut pan. This will make exactly 4-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.