Add milk, sugar, and butter to a small saucepan and heat on medium-low until butter is melted and sugar is dissolved.
In a small bowl combine eggs, mashed potato, and sourdough starter and combine well.
In a large bowl add flour and salt and combine well.
Add warmed milk mixture to flour and combine well.
Ensure the dough is not too hot so it doesn't kill the sourdough starter bacteria (you may need to wait a few minutes), then add the sourdough starter, potato and egg mixture to the rest of the dough. Combine well.
Wet hands and knead the dough in the bowl for about 5 minutes until a smooth, wet dough is formed.
Cover bowl with a lid or plate and let ferment at room temperature for about 5 hours.
After 5 hours at room temperature, transfer the dough to the refrigerator. Place a wet cloth on top of the bowl, or cover with plastic wrap to ensure the dough doesn't dry out.
Allow to long ferment in the refrigerator for at least 6 hours, or over night.
Cut cold dough in half, then roll out onto a piece of wax paper until 1/2 inch thick.
Using a doughnut cutter or jar lid and small cap, cut donut shapes into flattened dough.
Re-use remaining donut scraps by adding them back into the dough and re-rolling out to a flat 1/2 inch thick round.
Repeat with the second half of the dough.
Heat a stainless steal pan with lard filled about 1 inch high once melted. To check if the lard is preheated, carefully splash a small amount of water. It will sizzle when it's ready. You don't want the lard to be too cool or the donuts won't poof up enough.
Carefully place the number of donuts that fit in the pan and cook on one side for about 1 1/2 - 2 minutes, or until golden brown on the bottom, then flip to the other side with a fork.
Cook on the other side for about 1 1/2 - 2 minutes, or until golden brown on the second side.
Place on a plate and let cool for about 5 minutes before glazing.
Dip into a bowl of glaze or topping of choice and place back on the plate to continue cooling for another 5 minutes.
Enjoy!