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

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

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 use a ziploc bag to pipe the batter into the 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 cooling rack.

For the glaze, in a medium saucepan over medium heat, warm the butter, brown sugar, and milk together. Whisk until combined and bring to a slow simmer for about 1 minute, then remove from heat.

Add the vanilla and powdered sugar to the glaze mixture and whisk until smooth. If needed, return to low heat to melt any powdered sugar chunks.

Place a wire rack over a baking sheet to catch drips. Dip the tops of the donuts in the glaze and place them back on the wire rack to set.

If the glaze firms up, reheat on low to melt before dipping again.

Store the donuts in an airtight container.