Place potatoes in a large saucepan and cover with water. Bring to a boil. Reduce heat; cover and cook for 15-20 minutes or until tender. Drain, reserving 1/2 cup cooking liquid; cool to 110°-115°. Discard remaining cooking liquid. Mash the potatoes while still hot.

In a large bowl, dissolve yeast in reserved cooking liquid. Add the mashed potatoes, milk, oil, sugar, eggs and salt. Add enough flour to form a soft dough. Place in a greased bowl, turning once to grease top.

Cover and let rise in a warm place until doubled, about 1 hour. Punch dough down; let rise again until doubled, about 20 minutes. Roll out on a floured surface to 1/2-in. thickness. Cut with a floured 3-in. doughnut cutter.

In an electric skillet or deep-fat fryer, heat oil to 375°. Fry doughnuts, a few at a time, until golden brown.

Dust the doughnuts with icing sugar. Best served warm.