I found this recipe a few years back and have used it over and over. These "doughnuts" do take some time but they are very good.
1 package active dry yeast, which usually equals 1 tblsp
1-1/2 cups warm water
1/2 cup sugar
1 teaspoon salt
2 large eggs
1 cup evaporated milk
7 cups flour
1/4 cup vegetable shortening
oil for deep frying
Put the warm water into a large bowl, then sprinkle in the yeast and a couple teaspoons of sugar and stir until thoroughly dissolved. Let proof for 10 minutes. Add the rest of the sugar, salt, eggs, and evaporated milk. Gradually stir in 4 cups of flour and beat with a wooden spoon until smooth and thoroughly blended. Beat in the shortening, then add the remaining flour, about 1/3 cup at a time, beating it in with a spoon until it becomes too stiff to stir, then working in the rest with your hands. Cover the bowl with plastic wrap and refrigerate overnight in a greased bowl.
Roll the dough out onto a floured board or marble pastry surface to a thickness of 1/8 inch, then cut it into rectangles 2-1/2 inches by 3-1/2 inches with a sharp knife.
Heat the oil in a deep fyer to 360 degrees. Fry the beignets about 2-3 minutes until both sides are golden brown. Frying 3 to 4 at a time (batch) turn them over in the oil with tongs once or twice to get them evenly brown. Drain each batch, place on a platter lined with several layers of paper towles, and keep warm in a 200 degree oven until ready to serve.
Serve beignets with powdered sugar and a hot drink.
Adapted from the Gumbo Pages