Beat eggs with sugar and vanilla till light.
Add potatoes and shortening.
Sift together dry ingredients; add alternately with milk to potato mixture, beating well.
Chill 3 hours.
Roll out half of dough at a time, keeping other half chilled.
Roll on floured surface to 3/8 inch thick.
Cut with floured 1 1/2-inch doughnut cutter; chill 15 minutes.
Fry in deep hot fat (375°) about 3 minutes or till brown, turning once; drain.
Dip in sugar.