Warm the milk (it should be the temperature of a baby's bath water) and pour into a stand mixer. Add the yeast and sugar. Smell for the yeasty smell that tells you your yeast is active.
Next add the salt, eggs and melted shortening (make sure it's not too hot so it won't kill the yeast).
Add one cup of flour and turn the mixer on. Continue mixing while adding flour a cup at a time until you've added 5 cups of flour total. Reserve the last cup of flour to add as needed.
Knead the dough for 8-10 minutes until it is slightly tacky to touch but clears the sides of the bowl. Check out this post for tips on how to know when the dough is ready. Add extra flour as needed (you may need up to 6 cups of flour but you may also be fine with 5 1/2 cups).
Transfer dough to a lightly oiled bowl, cover it and let it rise until doubled in size, about 1 to 1 1/2 hours.
On a very lightly floured surface (you may not need any flour at all), dump the dough out and roll out until about 1/4 inch thick.
Use a circle cutter or the top of a mason jar or bowl to cut out donuts. Cut out a small circle in the center of the donut and transfer to a baking sheet to rise.
Cut out donut holes and make apple fritters with the donut scraps if desired (instructions for the apple fritters are in the blog post).
Let rise again until puffy and almost doubled in size.