For the Donuts:

1. Preheat the oven to 325°F and spray a donut pan with nonstick spray. Whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt in a medium bowl.
2. Whisk together the pumpkin, sugar, egg, oil, and vanilla in another bowl. Slowly fold the dry ingredients into the wet and mix until just combined.
3. Spoon the batter into the prepared pan, filling each donut well about ¾ full. Alternatively, you can use a piping bag to fill the pan.
4. Bake the donuts for 15-20 minutes or until the donuts are set and spring back slightly when lightly pressed. Cool the donuts in the pan for 10 minutes and then transfer to a cooking rack to cool completely.

For the Bourbon-Maple Glaze:

1. Place the maple syrup in a small pot over medium heat. Bring to a simmer and cook until it is reduced by roughly half.
2. Whisk in the bourbon and then the butter until it is completely smooth and melted.
3. Remove the pot from the heat and whisk in the powdered sugar, a little at a time, mixing until a smooth glaze forms. Stir in the salt and allow the glaze to cool slightly.
4. Dip each donut in the warm glaze and return them to the cooling rack to sit until the glaze has set, about 10 minutes.