Preheat oven to 350 degrees.
In a large bowl, whisk together the first seven dry ingredients, flour through sugar.
Make a well in the center and add the melted and cooled butter, vanilla, eggs, pumpkin, and milk. Mix gently.
Transfer mixture to a large baggie with the tip cut off. This makes it easy to pipe into the donut maker.
Fill each well ¾ full without covering the middle section. If you do, your doughnuts won't have a hole.
Cook for about 8-10 minutes.
Allow to cool and make the frosting.
Mix frosting ingredients in a small bowl. Adjust the amount of milk to your liking. More milk = thinner icing.