Heat the oven to 350°F (175°C) and grease two standard six-cavity donut pans, or grease one pan if you plan to bake in batches.

Whisk the flour, baking powder, baking soda, salt, pumpkin pie spice, and optional cinnamon together in a medium bowl.

In a separate large bowl, whisk the brown sugar, granulated sugar, egg, pumpkin purée, melted butter or oil, vanilla, and milk until smooth.

Add the dry ingredients to the pumpkin mixture and stir just until no dry streaks remain. Do not overmix the batter.

Transfer the batter to a piping bag or zip-top bag with one corner snipped off. Pipe the batter into the donut cavities, filling each about two-thirds to three-quarters full.

Bake for 10–15 minutes, until the donuts spring back when lightly pressed and a toothpick comes out clean or with a few moist crumbs.

Cool the donuts in the pan for about 5 minutes, then transfer them to a wire rack. For cinnamon sugar, brush warm donuts with melted butter and toss them in the cinnamon-sugar mixture.

For glaze, whisk the powdered sugar, milk or cream, vanilla, and salt until smooth. Dip cooled donuts into the glaze and let them set on a rack.