Mix water, sugar, and yeast in a large bowl and let sit for 10 minutes.
In another bowl, beat the eggs, salt and evaporated milk together. Mix egg mixture to the yeast mixture. In a separate bowl, measure out the bread flour. Add 3 cups of the flour to the yeast mixture and stir to combine. Add the shortening and continue to stir while adding the remaining flour. Remove dough from the bowl, place onto a lightly floured surface and knead until smooth. Spray a large bowl with nonstick spray. Put dough into the bowl and cover with plastic wrap or a towel. Let rise in a warm place for at least 2 hours.
Preheat oil in a deep-fryer to 350 degrees F.
Add the confectioners' sugar to a paper or plastic bag and set aside.
Roll the dough out to about 1/4-inch thickness and cut into 1-inch squares. Deep-fry, flipping constantly, until they become a golden color. After beignets are fried, drain them for a few seconds on paper towels, and then toss them into the bag of confectioners' sugar. Hold bag closed and shake to coat evenly.