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

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

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, then fold everything together gently just until combined and no flour pockets remain.

Spoon the batter into the donut cavities or transfer the batter into a large zipped-top bag. Cut a corner off the bottom of the bag and pipe the batter 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 your finger into the top of the donut. If the donut 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 mini donuts, bake in a mini donut pan for 8–9 minutes. Cool donuts for at least 10 minutes before icing them.

Combine the 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. Allow to simmer for 1 minute, then remove from heat and whisk in the vanilla extract and sifted confectioners’ sugar until smooth and combined.

Taste, then add a pinch of salt if desired. Let the icing cool for 5 minutes to slightly thicken.

Dip the tops of the pumpkin donuts into the warm icing. If the icing is getting too thick, whisk in a little more milk, or warm back up to thin it out.

Place dipped donuts on a cooling rack on a baking sheet to allow excess icing to drip off. Top with chopped nuts or other toppings if desired.

Cover leftover donuts tightly and store at room temperature for 1–2 days or in the refrigerator for up to 1 week.