Preheat the oven to 350°F. Lightly spray a donut pan, or mini muffin pan, with non-stick spray. Set aside.
In a large bowl, whisk together the oil, eggs, sugar, pumpkin puree, and pumpkin pie spice until well combined. Add the salt, baking powder, and flour and stir until just combined.
Spoon the batter into the prepared pan, filling to 3/4 full. For a regular donut pan, it’s a scant 1/4 cup in each donut well; for a mini muffin pan it’s 1 tablespoon per well. Smooth the batter out in the donut pan. Bake for 18-20 minutes for donuts, 20-22 minutes for donut holes, or until a toothpick inserted in the center comes out clean.
Allow the donuts to cool for 5 minutes before turning them out on a wire rack. While they cool, make the glaze.
In a small saucepan over medium heat, melt the butter and whisk in the maple syrup. Whisk in the powdered sugar until smooth and remove from the heat. Add 1-2 tablespoons of milk to thin the glaze.
Once the donuts have cooled for about 10 minutes, dunk them in the glaze, coating both sides. Place them on a wire rack for the glaze to set. If you want to sugar them instead, place the sugar and cinnamon in a plastic bag and add the donuts, one at a time, to the bag, shaking them gently to coat.
Donuts are best fresh but keep well for 2-3 days. Don’t keep them in a sealed container as they are very moist and will get overly sticky. They are best if left uncovered. They can also be frozen, but add the glaze or sugar after thawing before you serve them.