Mix the water, sugar, and yeast in the bowl of your stand mixer and let sit for 10 minutes.
In another bowl, beat the eggs, salt and evaporated milk together. Add the egg mixture to the yeast mixture.
Add 3 cups of flour to the yeast mixture and stir to combine. Add the shortening and continue to mix on low while adding the remaining flour. Increase the speed and knead dough until smooth.
Put the dough into a greased bowl and cover with a towel. Let rise in a warm place for 2 hours.
Pour about 3 inches of oil into a large skillet and heat over medium heat to 350 degrees.
Add the powdered sugar to a paper bag or large bowl and set aside.
Roll the dough out to about 1/4-inch thick and cut into 1-inch squares. Deep-fry, flipping the dough often, until they become a golden color.
Remove from the oil and drain them for a few seconds in a paper towel lined dish.
Toss the beignets into the bag or bowl of powdered sugar and toss to coat.
Continue frying until all donuts are done.