Heat water to 110º - 120º F in a in a medium glass bowl in the microwave. Stir in 1 tablespoon of the granulated sugar until it dissolves. Sprinkle the yeast into the water and sugar and allow to sit for about 5 -10 minutes to foam as it proofs.
While yeast is proofing, mix together remaining granulated sugar, eggs, salt, and evaporated milk together. Stir together the yeast mixture with the egg mixture. Then, stir in 3 cups of flour, one half cup at a time, into the yeast and egg mixture. Stir together until all the flour is well incorporated, being sure to get all of the flour incorporated from the bottom of the bowl. Add the shortening and continue to add the remaining flour until all of the flour is well combined.
Using the dough hook on your stand mixer, knead the dough, adding flour ¼ cup at a time until the the dough forms a ball and does not stick to the bottom of the bowl.
If using a stand mixer, fit the mixer with a dough hook and turn the mixer to medium speed and knead for 7-10 minutes. The dough should be tacky but not sticky.
If kneading by hand, place the dough onto a lightly floured surface and knead until smooth, about 10-15 minutes.
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 until it has doubled in bulk.
Once dough is ready, preheat the oil in a deep-fryer to 350º F. You will need enough oil to fully submerse the beignets as they are frying.
Line a rimmed baking sheet with two layers of paper towels for the beignets to drain on once deep fried.
Roll the dough on a lightly floured surface to about 1/4-inch thick. Cut the dough into 1-inch squares. Carefully add a few beignets to the heated oil at a time to deep fry. Flip the beignets constantly while cooking until they become a nice golden color. Remove them with a slotted spoon to dry on the paper towel lined pan for a few seconds. Then place them on a plate or tray and dust both sides with confectioner's sugar.
Total time does not include inactive time for dough to double in bulk, about 1 - 2 hours.