In a small bowl, whisk the yeast, water, and sugar and let sit until frothy, about 5 minutes.
In a large bowl or mixer, combine the yeast mixture with the egg, salt, and evaporated milk. Blend in about half the flour, then add the shortening and blend in well, then add the rest of the flour. Knead to dough for 2-3 minutes. You want the dough to be soft but not sticky. Add small amounts of flour as needed. It's best when the dough just barely stops sticking to the side of the bowl or mixer.
Place dough in a lightly greased bowl, cover loosely and let the dough rise in the fridge at least 3 hours or overnight.
Punch down the dough and place it on a lightly floured surface. Roll the dough out into a large square measuring 12"x12". Dough should be about 1/2" thick.
Using a knife or pizza cutter, cut the dough into 2-inch squares for mini beignets. For full-size beignets make 4-inch squares.
Remove squares to a cookie sheet sprayed with non stick cooking spray and loosely cover with plastic wrap. Let the squares rise for 30 to 40 minutes.
Pour vegetable oil into a deep fry pan over the stove on medium high to heat. Start this process while the dough is rising because it will take a little while to heat. When oil is hot (360℉-365℉), test a small piece of dough in the oil to make sure it's hot enough, the dough should float to the top and begin to brown within a few seconds.
Prepare by setting out a cookie sheet topped with paper towels and a large slotted spoon near the stove, these cook quickly! Also fill your paper bag with about a cup of powdered sugar.
Carefully place 3-4 pieces of dough in the oil, when you see the edges turning golden (about 45 seconds), quickly flip them over and cook for another 35-45 seconds.
Use a slotted spoon to remove dough from the oil and place on the paper towels. Let it rest for about 30 seconds.
Toss beignets into the paper bag filled with powdered sugar two at a time.
Seal the top and shake to coat. Add more powdered sugar as needed as you go.
Remove beignets to a plate or cooling rack and serve immediately, they taste best warm! Serve with caramel, chocolate sauce or raspberry preserves.