Begin by activating the yeast. In the bowl of a stand mixer with the dough hook (or large mixing bowl) attachment add the warm water, yeast and pinch of sugar. Stir and set aside until the yeast has dissolved, about 10 minutes.
To the bowl add the 1/4 cup of sugar, salt, egg, and the evaporated milk. With the mixer on low, add half the flour and mix until just combined. Add the shortening, and then gradually add the remaining flour until the dough forms into a mass. Turn off the mixer and transfer to floured surface. Add more flour, if needed, until you have an even, medium-textured (it should be pretty firm) dough. Add the dough to a large buttered bowl and cover with plastic wrap. Let the dough rest for at least 3 to 4 hours, or overnight in the refrigerator.
Once rested, gently turn the dough out onto a lightly floured surface. Sprinkle a little more flour on top so you can work with the dough. Gently shape the dough into a 1-inch thick rectangle so it can be cut into squares. Using a sharp knife or pizza cutter cut into squares, (you should yield 12 large squares, depending on how thick you rolled the dough).
Preheat the oven to 250 degrees F.
Heat about 3 inches of oil in a large, heavy-based pot over medium heat, (you want to make sure there is plenty of room as the beignets will puff up when cooked) to 350 degrees F. Fry the beignets in batches, about 3 minutes per batch. Turn them in the oil while they fry to brown evenly on both sides. Remove from the oil a paper towel lined sheet pan and keep warm in a low oven while you cook the remaining dough. To serve, transfer beignets to a serving platter and dust generously with powdered sugar.