In a large bowl, stir together 3 cups flour and yeast. In a small saucepan, heat on medium-low and stir evaporated milk, water, granulated sugar, shortening, and salt just until shortening is almost melted.
Add milk mixture to flour mixture. Add 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 dough in a greased bowl; turn once to grease the surface. Cover and refrigerate dough for 4 to 24 hours.
Turn dough out onto a lightly floured surface. Cover; let rest 10 minutes. Roll into an 18-by-12-inch rectangle; cut into 36 3-by-2-inch rectangles. Cover; let rest 20 minutes (dough will not double).
Heat oven to 300°F.
Heat 3 inches of oil in a deep saucepan. Fry a few dough rectangles at a time in hot oil about 1 minute or until beignets are golden brown on both sides, turning once. Drain on paper towels. Keep warm in oven while cooking remaining beignets. Generously sift powdered sugar over beignets.
Serve warm. Makes 3 dozen.
Approximate Nutrient Analysis per Beignet (not including powdered sugar):
170 calories, 8 g fat, 1 g saturated fat, 10 mg cholesterol, 75 mg sodium, 20 g carbohydrate, 1 g fiber, 4 g sugar, 3 g protein