Preheat your oven to 350°F (175°C). Grease a donut pan or two with non-stick cooking spray.
In a large mixing bowl, combine the oil and brown sugar. Mix until well combined.
Add the pumpkin puree, eggs, and vanilla extract to the sugar and oil mixture. Mix until everything is well combined.
Next, add in the flour, pumpkin pie spice, baking soda, baking powder, and sea salt. Be careful not to overmix; just mix until no large lumps remain.
Spoon or pipe the donut batter into the greased donut pans, filling each cavity about 2/3 full. I like to add my mixture to a gallon ziploc bag and then cut a small hole in the bottom corner to pipe it that way.
Bake in the preheated oven for 12-15 minutes, or until the donuts spring back when lightly touched and a toothpick inserted into the center comes out clean.
While the donuts are baking, prepare the cinnamon sugar coating. In a small bowl, mix together the granulated sugar and ground cinnamon.
When the donuts are done baking, remove them from the oven and let them cool in the pan for a few minutes.
Carefully remove the donuts from the pan and dip each one into the melted butter, then roll it in the cinnamon sugar mixture to coat it evenly.
Place the coated donuts on a wire rack to cool completely. Enjoy your homemade baked pumpkin donuts!