Boil first two ingredients together for five minutes. Pour into bread machine and cut with the 1/4 cup of cold water.
Turn machine on and quickly add dry ingredients, starting with sugar and ending with yeast. (This takes the intense heat off the boiled shortening/water mix so it doesn't kill the yeast and curdle the egg.) Add the egg just after the yeast and allow the bread machine to knead the dough for the full dough cycle.
Remove dough from pan to a flour-dusted surface and roll thin. Cut into squares and fry in hot oil just long enough for them to golden brown.
Drain and serve sprinkled with powdered sugar.
Tip: Beignets puff up two inches thick or more, so you need at least a couple of inches of oil in your pan.