1 pound russet potatoes, peeled and quartered
2 (1/4 ounce) packages active dry yeast
1 1/2 cups warm milk (110 to 115 degrees F)
1/2 cup vegetable oil
1/2 cup granulated sugar
2 eggs
1 teaspoon salt
7 1/2 cups all-purpose flour
Oil for deep-fat frying
4 cups confectioners sugar
1/3 cup water
1 teaspoon vanilla extract

Place potatoes in a saucepan and cover with water. Bring to a boil; cook until tender. Drain, reserving 1/2 cup cooking liquid. Cool to 110 to 115 degrees F.

Discard remaining cooking liquid. Mash potatoes without milk or butter.

In a large mixing bowl, dissolve yeast in reserved cooking liquid. Add 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 inch thickness. Cut with a floured 3-inch doughnut cutter.

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

Combine confectioners' sugar, water and vanilla extract; dip warm doughnuts in glaze. Cool on wire rack.

Yields 4 dozen.