In a stand mixer fitted with a dough hook attachment, pour the lukewarm water, sugar, and yeast into the bowl. Mix until blended. Set aside for 10 minutes.
In a medium bowl, lightly beat the eggs with a whisk. Add the evaporated milk and salt, beat until blended.
Pour the egg mixture into the yeast mixture after 10 minutes. Add 3 cups of bread flour and the shortening. Mix on medium-low speed until well combined. As a dough starts to form, add the remaining bread flour, mixing on medium speed. Continue to mix until a dough forms. The dough will be sticky.
Prepare a lightly floured surface. Rub flour on your hands and remove the dough from the stand mixer. Knead the dough until it is soft and smooth, about 3 minutes.
Next, lightly butter a large bowl. Place the dough into the buttered bowl, and cover with plastic wrap. Allow the dough to rise for 2 hours.
After the dough has risen, in a large pot, heat the cooking oil to 350 degrees over medium-high heat.
While the oil is heating, prepare a lightly floured surface to roll out the dough. Punch the dough down with your fist and turn it out onto the floured surface. Lightly flour a rolling pin, and roll the dough out to about a 1/4-inch thickness and cut into 2-inch squares.
Working in batches, carefully deep-fry the dough, approximately 2 minutes per side or until golden brown. Using a slotted spoon or a pair of tongs remove fried beignets onto a plate lined with paper towels to drain the excess oil.
While the beignets are cooling, pour powdered sugar into a large plastic container. Place the beignets into the container and secure with the cover of the container. Shake vigorously until the beignets are coated evenly. If you do not have a container, you may use a paper bag. Serve immediately. Enjoy!
Substitute all-purpose flour for bread flour if you do not have bread flour on hand. Bread flour will yield chewier beignets due to higher protein content.
If you notice your beignets are flat rather than puffy, your oil may not be hot enough.
If you prefer your beignets to be less sweet, simply use a sieve to provide a light dusting of powdered sugar.
If your dough is too thick, rather than using a rolling pin, stretch out individual pieces using your hands.