Combine the Yeast, Water, and Sugar in the work bowl of a stand mixer fitted with a dough hook (You could also make this in a food processor, or the old fashioned way, by hand). Let this sit until frothy, about 5 minutes, then add the Salt, Egg, and Evaporated Milk.
Mix on low speed, then add half of the flour until it starts to come together, then add the shortening. When the shortening is incorporated start adding the remaining flour, a little at a time until most of it is incorporated. At this time I always turn the dough onto a floured bench to finish by hand, just like when I make bread; it's a touch thing. Knead the dough adding just enough flour as necessary to make a non-sticky, smooth dough. Place the dough into a large oiled bowl, loosely cover and let rise about 20 minutes. I put mine in a barley warm oven.
After the dough has doubled in bulk, punch it down and turn it onto a floured surface and roll out into a rectangle that is about 1/2" thick. With a very sharp knife working at a diagonal to the rectangle, cut into 2" wide strips. Now cut into diamond shapes by making diagonal cuts in the opposite direction.
Place the Beignets on a floured baking sheet to let rise about 40 minutes in a warm place (I place them in a barely warm oven).
When the Beignets have risen, heat 2-3 inches of vegetable oil in a large saucepan to 350-360 degrees. Place 2-3 Beignets into the hot oil at a time, being careful not to smash or deflate them. When they are golden brown, flip them over until golden brown on the other side (They go pretty quickly so start checking them right after they go into the oil). Remove to paper towel lined plates to drain. Serve hot topped with plenty of powdered sugar (because the dough doesn't contain much sugar, you will want a lot!). Best served with Cafe au Lait. Enjoy!