From New Orleans' French Quarter coffee houses, beignets are square hole-less fried dough that are airy and delicate. Use a deep saucepan to fry the beignets, leaving at least 3 inches between the oil and the top of the pan. Roll in powdered sugar and serve warm for breakfast, brunch, or dessert.
In a large bowl, stir together 1-1/2 cups of the flour, the yeast, and nutmeg. In a small saucepan, heat and stir milk, granulated sugar, the 2 tablespoons shortening, and the salt just until warm (120 degree F to 130 degree F) and shortening is almost melted.
Add milk mixture to flour mixture; add egg. Beat with an electric mixer on low to medium speed for 30 seconds, scraping side of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in enough of the remaining flour to make a soft dough.
Place dough in a greased bowl; turn once to grease surface. Cover; refrigerate for at least 4 hours or up to 24 hours.
Punch down dough. Turn dough out onto a lightly floured surface. Cover; let rest for 10 minutes. Roll into a 15x12-inch rectangle; cut into thirty 3x2-inch rectangles. Cover; let rest for 20 minutes (dough will not double in size).
In a heavy, deep saucepan, heat 3 inches of shortening to 375 degree F. Fry dough rectangles, a few at a time, in deep hot fat about 1 minute or until beignets are golden, turning once. Using a slotted spoon, remove beignets and drain on paper towels. Keep warm in a 300 degree F oven while frying remaining beignets. If desired, sprinkle with powdered sugar. Makes 30 beignets.