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 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 it 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 together in a medium saucepan over medium heat, whisking until combined and bringing to a slow simmer. Simmer for about 1 minute, then remove from heat.

Add the vanilla and powdered sugar to the mixture, whisk until smooth. If the mixture has chunks, return it to low heat and stir until smooth.

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, place back on low heat to melt again and continue dipping.