Combine yeast, 1/2 cup warm water, and 1 tsp. granulated sugar in a mixing bowl and let stand for 5 minutes to activate the yeast.

Add evaporated milk, eggs, salt, and remaining granulated sugar to the yeast mixture.

Microwave the remaining 1 cup of water until hot, then stir in the shortening until melted. Add this mixture to the yeast mixture.

Gradually add 4 cups of flour and beat until smooth. Gradually add the remaining 2 1/2 to 3 cups of flour, beating until a sticky dough forms.

Transfer the dough to a lightly greased bowl, turning to grease the top. Cover and chill in the refrigerator for 4 to 24 hours.

Turn the chilled dough out onto a floured surface and roll it to 1/4-inch thickness.

Cut the dough into 2 1/2-inch squares.

Pour oil to a depth of 2 to 3 inches into a Dutch oven and heat to 360°F (180°C).

Fry the dough squares in batches for 2 to 3 minutes on each side, or until golden brown.

Drain the fried beignets on a wire rack.

Dust the beignets immediately with sifted powdered sugar.