In a large bowl, stir together 3 cups of the flour and the yeast. In a small saucepan, heat and stir evaporated milk, water, granulated sugar, shortening, and salt just until warm (120 degrees F to 130 degrees F) and the shortening is almost melted.
Add milk mixture to the flour mixture. Add the eggs. Beat with an electric mixer on low speed for 30 seconds, scraping bowl. Beat on high speed for 3 minutes. Using a wooden spoon, stir in enough of the remaining flour to make a soft dough.
Place the dough in a greased bowl; turn once to grease the surface. Cover and refrigerate the dough for 4 to 24 hours.
Turn dough out onto a lightly floured surface. Cover; let rest 10 minutes. Roll into an 18x12-inch rectangle; cut into thirty six 3x2-inch rectangles. Cover; let rest 20 minutes (dough will not double).
Heat 3 inches of oil in a deep saucepan to 375 degrees F. Fry a few dough rectangles at a time in deep hot oil about 1 minute or until beignets are golden brown on both sides, turning once. Drain on paper towels. Keep warm in a 300 degree F oven while cooking remaining beignets. Generously sift powdered sugar over beignets. Serve warm. Makes 4 dozen.