1. Place potatoes in a saucepan and cover with water
2. Bring to a boil; cook until tender
3. Drain, reserving 1/2 c cooking liquid; cool to 110-115 degrees
4. Discard remaining cooking liquid
5. Mash potatoes without milk or butter
6. In a large mixing bowl, dissolve yeast in reserved cooking liquid
7. Add mashed potatoes, milk, oil, sugar, eggs and salt
8. Add enough flour to form a soft dough
9. Place in a greased bowl, turning once to grease top
10. Cover and let rise in a warm place until doubled, about 1 hour
11. Punch dough down; let it rise again until doubled, about 20 minutes
12. Roll out on a floured surface to 1/2" thickness
13. Cut with a floured 3-in doughnut cutter.
14. In an electric skillet or deep-fat fryer, heat oil to 375.
15. Fry doughnuts, a few at a time, until golden brown
16. For glaze, combine confectioners' sugar, water and vanilla in a bowl
17. Dip warm doughnuts in glaze. Cool on wire racks
Yield: 4 dozen