Preheat oven to 350 degrees. Spray a donut pan with nonstick spray.

Stir the flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice together in a large bowl until mixed.

In another bowl, mix together the oil, brown sugar, eggs, pumpkin, milk, and vanilla until combined.

Pour the wet ingredients into the dry ingredients and gently mix until just combined.

Spoon the batter into the donut pan or place the batter into a ziploc, cut off the corner, and pipe into the donut pan.

Bake for about 10 minutes, then remove from the oven and let cool in the pan for 2 minutes. Remove from the pan and let cool on a wire rack.

For the glaze, warm the butter, brown sugar, and milk in a medium saucepan on medium heat. Whisk until combined and bring to a slow simmer, letting it simmer for about 1 minute.

Remove from heat, add the vanilla and powdered sugar, and whisk until smooth. Return to low heat if needed to melt any powdered sugar chunks.

Place a wire rack over a baking sheet or parchment to catch excess drip. Dip the tops of the donuts in the glaze and place back on the wire rack to set.

If the glaze starts to firm up, return it to low heat to melt again before dipping.