In a mixing bowl, combine yeast, sugar and water. Stir to mix. Keep in a warm area for 10 minutes.
Scald milk , add shortening, sugar and salt. Cool to lukewarm then mix in 3 eggs.
Now add the yeast mixture and about 3 1/2 cup flour. Mix thoroughly, let rise until doubled in bulk.
Roll out, cut with donut cutter. Place them on parchment paper or wax paper.
Let them rise, covered, for an hour or until double in height. Knead the scraps of dough into a ball and let them rest covered for about 20 minutes before rolling out again and making more donuts. Fry the donuts in oil at 360 degrees.
Turn to brown both sides. Remove to a rack and brush with confectioners' sugar mixed with water to glaze.
Best served warm.