In a medium-size bowl, add the warm water, sugar, and yeast and whisk well to combine. Set aside for about 10 minutes, or until the mixture has bubbled up and become foamy.
In the bowl of a stand mixer fitted with the paddle attachment, beat the egg until smooth. Beat in the vanilla and evaporated milk. Beat in 1 ¾ cup of flour until smooth. Turn the mixer to low speed and slowly pour in the yeast mixture being careful of splashing. Beat until smooth. Add the butter and beat until incorporated. Finally, beat in the remaining flour (1 ¾ cup) and salt. Beat until the dough is smooth and cohesive; about 2 minutes. Cover the bowl tightly with plastic wrap and refrigerate for at least 2 hours or up to 24 hours.
Set a cookie cooling rack in a baking sheet and set to the side.
Put oil in a cast iron pan, about 4-inches, and heat to 360º F. Remove the dough from the refrigerator and place on lightly floured surface. Roll the dough out into a ¼ inch thick rectangle and cut into 2 ½ inch squares.
In batches, fry the dough until they puff up and are golden brown in color, about ½ minute a side. With a slotted spoon, transfer the beignets to the cooling rack and repeat.
While still warm (but not hot from the oil) roll batches of the beignets in a bowl of confectioners’ sugar to coat and return to the rack to continue cooling or to a plate and serve ... this is the best way.