Combine 1 1/2 cups flour, sugar, yeast, and salt in a large bowl, mix well.
Combine milk, butter, and shortening in a saucepan; heat until very warm (120° to 130°), stirring until butter and shortening melt.
Add milk mixture to flour mixture, beat at medium speed of an electric mixer 2 minutes.
Add egg and 1 1/2 cups flour.
Beat 2 minutes.
Stir in remaining flour.
Turn dough out onto a lightly floured surface, and knead 3 or 4 times.
Place mixture in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, about 1 hour and 10 minutes or until doubled in bulk.
Punch dough down, turn out onto a lightly floured surface.
Knead 3 or 4 times.
Divide dough into thirds.
Cover 2 sections, and set aside.
Roll remaining section out to 1/4 to 1/4-inch thickness, cut into 2-inch squares.
Repeat with remaining sections.
Heat 3/4 to 1 inch of oil to 375°.
Gently pull outside edges of each square so center is thinner than edges.
Drop 4 dough squares at a time into hot oil.
Cook on each side until golden.
Drain, and sprinkle with powdered sugar.