Preheat oven to 350 °F. Grease 2 standard donut pans and set aside.
In a medium mixing bowl, mix well to combine the flour, baking powder, salt, and pumpkin pie spice. Set aside.
In a large mixing bowl, mix well to combine 3 eggs, pumpkin, granulated sugar, brown sugar, and butter.
Add the dry ingredients to the wet ingredients and stir until just combined.
Using a spoon, distribute the batter evenly between the greased donut pans, filling each donut mold about 3/4 of the way.
Bake for 12-15 minutes or until a toothpick inserted into the doughnuts comes out clean.
Remove from the oven and allow to cool in pan for 5 minutes before carefully loosening the donuts from the pan and transferring to a cooling rack.
In a small bowl, stir to combine the powdered sugar, milk, and vanilla. Dip the donuts into the glaze one at a time then place on a wire cooling rack to allow the excess drip off.
Notes
Although these are best served freshly baked, you can store them in an airtight container for up to 2 days at room temperature. Or for up to 4 days in the refrigerator.If the glaze is too thin, add a bit more powdered sugar. If the glaze is too thick, thin it out with a touch more milk.