Proof your yeast by adding it to the warm water. Mix it up and let it rest.
Scald the milk in your microwave or on top of your stove, and let cool. I learned from a baker that the reason you scald the milk is because regular milk has an enzyme in it that will kill the yeast. If you don't scald it first to kill the enzyme, your donuts won't rise.
Combine yeast, milk, sugar, salt, eggs, shortening and 3 cups (375g) flour.
Beat on low for 30 seconds, scraping bowl constantly. I used a Kitchenaid stand mixer, but a handheld mixer will work too.
Beat on medium speed for 2 minutes, scraping bowl occasionally.
Carefully (not like me), stir in remaining flour until smooth.
Cover and let rise until double, 30-60 minutes, depending on the yeast you used. I went the full 60, and you can see in step 4 what happened! (I would do it again, they were great!)