In a measuring cup combine the water, yeast, and 1 teaspoon sugar. Let sit until the yeast gets frothy and smells yeasty.
In the bowl of an electric mixer, combine the flour, remaining 1/2 cup sugar, and pinch salt.
In another bowl, combine the egg yolks, evaporated milk, melted butter, and vanilla. Add the yeast mixture and whisk to combine well.
Add the wet mixture to the dry ingredients and place on the stand mixer fitted with a dough hook. Once the ingredients are well combined, knead 5 minutes. Remove the bowl from the mixer, cover, and place in a warm area for 2 hours, or until the dough has doubled in size.
In a wide, deep pot, heat the oil to 350 degrees F.
Remove the dough from the bowl and lightly knead on a floured work surface. Cut the dough into 2-inch squares.
Set up a paper towel-lined sheet tray to land the beignets when they come out of the oil.
Working in batches so as to not crowd the oil, fry the dough squares until they are puffy and golden brown. Remove from the oil, make a pit stop on the paper towels and immediately dust with powdered sugar.