In a large mixing bowl whisk together ¾ cup lukewarm water and 1 teaspoon active dry yeast. Set aside about 10 minutes, until the mixture is frothy.
In a medium bowl whisk together ¼ cup granulated sugar, 1 large beaten egg, and ½ cup evaporated milk. Pour this sugar-egg-milk mixture into the frothy yeast mixture and whisk to combine.
In a separate medium bowl whisk together 3 ½ cups bread flour and 1 teaspoon salt. Add the flour mixture to the wet mixture in roughly 1-cup increments, stirring after each addition until the dough begins to come together and no dry streaks remain.
Lightly flour a clean work surface and turn the dough out onto it. Knead the dough by hand until smooth and elastic, about 10 minutes.
Shape the kneaded dough into a ball and place it back into the mixing bowl. Cover with a clean kitchen towel and set the bowl in a warm, draft-free place. Let the dough rise until doubled in size, about 1½ to 2 hours.
When the dough has doubled, pour about 2 quarts of vegetable oil into a large, deep pot or prepare your deep fryer. Heat the oil over medium-high heat until it reaches 350°F.
While the oil heats, turn the risen dough onto a lightly floured surface and roll it into a large rectangle about ¼–½ inch thick. Cut the dough into approximately 2-inch squares.
Working in batches of 3–4 pieces (do not overcrowd the oil), carefully drop the dough squares into the hot oil. Fry until golden brown on the first side, about 2 minutes, then flip and fry the second side about 2 minutes more. Maintain the oil temperature near 350°F.
Use a spider strainer or slotted spoon to remove the beignets from the oil and transfer them to a paper towel–lined baking sheet or plate to drain.
Let the beignets cool about 1 minute, then toss them in 1 ½ cup powdered sugar until coated (use more powdered sugar as needed). Serve warm with chocolate or caramel syrup for dipping, if desired.