Pour ½ cup room temperature water into a small bowl. Sprinkle the yeast over the water. Let yeast dissolve for 5 minutes.
In a large bowl, combine the shortening, sugar, and salt. Pour the boiling water over the shortening mixture, then stir in the evaporated milk and vanilla extract. Let the mixture cool down until it is lukewarm, then add the yeast and water mixture and beaten eggs.
Slowly mix in the flour until the dough forms a ball. You may want to use a dough hook. Cover the dough with plastic wrap and refrigerate for 30 minutes to 1 hour. I put mine in the freezer for 15 minutes.
Working with a baseball sized portion at a time, roll out the dough ⅛-inch thick. Cut the rolled out dough into 2½ inch squares.
Heat your oil for frying in a deep and wide skillet over medium-low-high heat. The temperature will depend on your stove and skillet.
Slowly slide dough into the oil to avoid splattering and deep fry until they puff up and turn a golden brown color. Place each beignet onto a rack with paper towels underneath. Dust beignets with confectioners' sugar. Serve warm.
Adapted from Costas French Market Doughnuts (All Recipes)
Recipe by at http://sophistishe.com/2014/03/nola-style-beignets/