Pour the yeast in to the warm water and let sit for 5 minutes or so. In a large bowl add salt, sugar, shortening, and milk. Let it cool down a little. Add the potatoes, eggs, yeast mixture to the milk mixture. Add the flour 1 cup at a time till it forms nice firm dough. Sprinkle some flour on your counter and roll out. Then cut your doughnuts. Let them raise for a good hour. Then heat some oil to 350 degrees and start frying.

Make a thin glaze with 2 cups of powdered sugar, 1 teaspoon of vanilla, and some water. Dip each doughnut in your glaze and set on a tray to cool.