DISSOLVE YEAST IN WARM WATER. COMBINE MILK, SHORTENING, SUGAR AND SALT, COOL UNTIL LUKEWARM. STIR IN YEAST, POTATOES AND EGGS. GRADUALLY ADD ENOUGH FLOUR TO MAKE A SOFT DOUGH. TURN ONTO FLOURED SURFACE. KNEAD UNTIL SMOOTH AND SATINY (ABOUT 7 MINUTES). PLACE IN LIGHTLY GREASED BOWL; TURN OVER TO GREASE TOP, COVER, LET RISE IN A WARM PLACE UNTIL DOUBLED (1-1 1/2 HOURS) ROLL TO 1/2 IN THICKNESS. CUT WITH DONUT CUTTER AND LET RISE UNTIL DOUBLED, ABOUT 30 MINUTES.
MEANWHILE MIX POWDERED SUGAR, WATER AND VANILLA (MIXTURE WILL LOOK LIKE THICK CREAM)
FRY IN DEEP HOT OIL, 375, TURNING ONLY ONCE. DRAIN ON PAPER SACK. DROP INTO GLAZE AND PLACE ON COOLING RACK UNTIL DRY
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