Dissolve the yeast and sugar in the warm water in a large mixing bowl, or the bowl of a stand mixer. Let the solution sit for 15 minutes and it will become foamy.

Whisk in the milk, egg and salt. Then mix in half of the flour with a large spoon. If using a mixer, use a paddle attachment on low to medium speed.

Mix in the shortening.

Place the dough in an oiled bowl covered with plastic wrap or a towel in a warm spot to rise for 2 hours. The dough will double in size.

Preheat 3 to 4 inches of cottonseed oil in a pan or deep fryer to 370 degrees F.

On a heavily floured surface, roll out the dough until it is 1/4-inch thick. Use a pizza slicer or knife to cut the dough into 2 1/2-inch square pieces and fry 3 to 4 pieces at a time in the oil. Immediately after dropping the dough into the oil use a large spoon to gently splash hot oil over the top of each piece. after 30 to 45 seconds, flip all of the beignets over and continue to baste with the oil. After another minute or so, flip the beignets again, and continue to cook until the beignets are a deep golden brown. Continue flipping the beignets over to brown them evenly on both sides. After about 3 minutes, they should be done. Let them drain on a cooling rack or a paper towel-lined plate for a minute, until you can handle them.

Serve three beignets on a plate with a very heavy dusting of powdered sugar on top.