Dissolve yeast in warm water in a large mixing bowl, stirring well; let stand 5 minutes or until bubbly. Add milk, egg, 1/4 cup sugar, and salt; beat well. Gradually blend in flour, mixing well. Cover with a damp cloth, and refrigerate overnight.
Turn dough out onto a heavily floured surface; roll to 1/4-inch thickness. Cut into 2 1/2-inch squares; let rest 10 minutes.
Heat 3 to 4 inches of oil to 375°; drop in 3 to 4 beignets at a time. Cook 1 minute or until golden brown on one side; turn and cook other side. Drain on paper towels; sprinkle with powdered sugar. Serve hot.