Allow the potatoes to cool and then mash in a large bowl with skins on until no chunks remain.
Add the eggs, and milk to the mixture and stir.
In a small bowl add the sugar and baking powder and whisk to combine.
Stir into the potato mixture then add the salt, shortening and vanilla.
Add the flour 1 cup at a time (you may only need 2 to 3 cups depending on how much potato you used) until a soft, slightly sticky dough forms.
Do not knead the dough.
Heat oil in a cast iron pot to medium high or 375 degrees.
Meanwhile, on a floured surface, roll out the dough, about 1/2" thick.
Cut out your donuts and with your hand very near the oil (trust me, it will be less of a chance to splash and burn this way) drop the donuts, a few at a time in the oil.
Turn constantly with a metal spider or slotted spoon until golden brown.
Drain on a plate with a paper towel and then immediately into cinnamon sugar or desired topping.