In a large bowl, dissolve yeast in warm water. Add sugar, salt, eggs, evaporated milk, and blend well. Mix in 4 cups of the flour and beat until smooth. Add the shortening, and then the remaining 3 cups of flour. Cover and chill for up to 24 hours.
Roll out dough 1/8 inch thick. Cut into 2 1/2 inch squares. Fry in 360 degree F (180 degrees C) hot oil. If beignets do not pop up, oil is not hot enough. Drain onto paper towels.
Shake confectioners’ sugar on hot beignets. Serve warm.