Preheat the oven to 350°F (177°C). Grease donut pan(s) with nonstick spray.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice until combined.

In a medium bowl, whisk together the oil, brown sugar, eggs, pumpkin puree, milk, and vanilla extract until combined.

Pour the wet ingredients into the dry ingredients and whisk gently until combined and no flour pockets remain. Do not over-mix.

Spoon the batter into the donut cavities or transfer batter to a large zipped-top bag, cut a corner off the bottom, and pipe into each donut cavity, filling each about halfway.

Bake for 10–11 minutes or until the edges and tops are lightly browned. To test, poke the top of the donut; if it bounces back, they’re done.

Cool donuts in the pan for 2 minutes, then transfer to a cooling rack. Re-grease the pan and bake the remaining donut batter.

For icing, combine brown sugar, milk, and butter in a medium saucepan over medium heat. Stir until the butter has melted and the mixture is smooth.

Bring to a simmer and allow to simmer for 1 minute, then remove from heat. Whisk in vanilla extract and sifted confectioners’ sugar until smooth. Add a pinch of salt if desired. Let cool for 5 minutes to thicken.

Dip the tops of the pumpkin donuts into the warm icing. If needed, whisk in more milk or warm it up to thin.

Place dipped donuts on a cooling rack to allow excess icing to drip off. Top with chopped nuts if desired. The icing will set in about 1 hour.