Preheat the oven to 350°F (177°C). Lightly grease a donut pan with nonstick cooking spray.

Add the flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice to a large mixing bowl. Whisk until the dry ingredients are evenly combined.

In a separate bowl, whisk the vegetable oil and brown sugar together. Add the eggs, pumpkin puree, milk, and vanilla, then whisk until smooth.

Pour the pumpkin mixture into the dry ingredients. Stir gently just until the batter comes together. Stop mixing as soon as you no longer see dry streaks of flour to help keep the donuts tender.

Transfer the batter to a piping bag or a large food-safe bag with one corner snipped off. Pipe the batter evenly into the prepared donut cavities, filling them approximately halfway.

Bake the Baked Pumpkin Donuts for about 10–11 minutes. They are ready when the tops spring back after being gently pressed.

Leave the donuts in the pan for about 2 minutes before carefully transferring them to a wire rack. Repeat with the remaining batter as necessary. Allow the donuts to cool before adding the icing.

To prepare the icing, place the brown sugar, milk, and butter in a small saucepan over medium heat. Stir until melted and smooth, then bring the mixture to a gentle simmer for about 1 minute.

Remove the saucepan from the heat. Whisk in the vanilla followed by the sifted confectioners’ sugar. Add a small pinch of salt and continue whisking until smooth.

Allow the icing to stand for approximately 5 minutes so it can thicken slightly.

Dip the top of each cooled donut into the warm brown sugar icing. If desired, immediately sprinkle with crushed walnuts.

Transfer the finished donuts to a wire rack and allow the glaze to set before serving or storing.