In large bowl, sprinkle yeast over water and stir to dissolve. Add sugar, eggs and milk. Blend with rotary beater.
Add 4 cups of the flour and beat smooth. Add shortening. Beat in remaining flour. Cover and chill several hours.
Deep fry at 360° for 2 to 3 minutes or until lightly browned on each side. If beignets don't rise to the top immediately when dropped into the oil, the oil isn't hot enough.
Drain on paper towels. Sprinkle heavily with powdered sugar.