1 (¼-ounce) envelope active dry yeast (2¼ teaspoons)
1½ cups warm water (105° to 115°), divided
½ cup granulated sugar
1 cup evaporated milk
2 eggs, lightly beaten
1 teaspoon salt
¼ cup vegetable shortening
6½ to 7 cups bread flour
Vegetable oil, for frying
Powdered sugar, for dusting
1. Combine the yeast, ½ cup warm water, and 1 teaspoon granulated sugar in the bowl of a heavy-duty stand mixer; let stand 5 minutes. Add milk, eggs, salt, and remaining granulated sugar.
2. Microwave remaining 1 cup water until hot (about 115°); stir in shortening until melted. Add to yeast mixture. Using the paddle attachment, beat at low speed, gradually adding 4 cups flour, until smooth. Switch to a dough hook and gradually add remaining 2½ to 3 cups flour, beating until a sticky dough forms. Transfer to a lightly greased bowl; turn to grease top. Cover and chill 4 to 24 hours.
3. When you're ready to fry the beignets, turn the dough out onto a floured surface; roll to ¼-inch thickness. Cut into 2½-inch squares.
4. Pour oil to depth of 2 to 3 inches into a Dutch oven; heat to 360°. Fry dough, in batches, 2 to 3 minutes on each side or until golden brown. Drain on a wire rack. Dust immediately with powdered sugar.