Peel and cube potatoes, then place potatoes in a large saucepan and fill with water until potatoes are completely covered by an inch.
Bring to a boil, then reduce heat and cook for 15-20 minutes, covered, until potatoes are tender.
Reserve 1/2 cup cooking liquid; discard remaining liquid.
Mash the potatoes with a potato masher, making sure to get rid of as many lumps as possible, but not over mixing. And set aside.
Get your kitchen thermometer out, and add your milk to your reserved liquid, adding until temperature reaches 110° (Note 1)
Pour liquid into the bowl of a stand mixer, and add your yeast. Dissolve yeast
Add the remainder of the milk to the mashed potatoes to help cool them. Use your kitchen thermometer to check the temp, and when it reaches 110 °, add the mashed potatoes, milk, 1/2 cup of canola oil, sugar, eggs and salt to the yeast mixture in your stand mixer bowl.
Using a stand mixer fitted with the dough hook, mix flour into the dough, a cup at a time to form a soft dough.
(Note 2)
Once mixed, place dough in a bowl greased with cooking spray or oil, turning once so the whole dough has a light coating of the oil. Then cover with plastic wrap. Place a dish towel over the plastic.
Let dough rise in a warm place until doubled, about 1 hour.
Punch dough down, then let the dough rise again until doubled, about 20 minutes.
Flour a work surface, and using your hands, tip dough out, and form a round of dough that is about 10 inches in diameter, and 1 1/2 inches thick.
Cut with a floured 3 -4 inch donut cutter. You should get roughly 12 large doughnuts (Note 3)
Put 6 cups of oil into a heavy bottomed pot or dutch oven, and heat to 350° F. Use a liquid/candy thermometer to check temp, and keep it at 350° F. (Note 4)
Fry donuts, two at a time, until dark golden brown, about 4 minutes per batch, rotating the donuts half way through. Do not allow the heat to exceed 350° F, the outside will cook too fast and leave the inside doughy. (Note 5)