Preheat oven to 350°F (175°C). Lightly grease a donut pan.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice.
In another bowl, whisk together the sugar, pumpkin purée, milk, yogurt, egg, vanilla, and melted butter/oil until smooth.
Add the wet ingredients to the dry ingredients and stir until just combined—don’t overmix.
Put pumpkin donut batter in a piping bag with no tip (or a plain round tip) and pipe the batter into the donut pan, filling each cavity about 3/4 full. Alternatively, you can spoon the batter in, but it gets a little tricky.
Bake for 10–12 minutes, or until the donuts spring back when lightly touched and a toothpick comes out clean.
Let cool for a few minutes in the pan, then transfer to a wire rack.
In a small bowl, whisk together the powdered sugar, maple syrup, milk, vanilla, and a pinch of salt. Adjust the consistency by adding more milk if needed—it should be thick but pourable.
Once the donuts are cool, dip the tops into the glaze and let the excess drip off. Set them back on a plate or wire rack and let the glaze set for 10–15 minutes before serving.