Yield 2 1/2 dozen.
1 package active dry yeast
3 tablespoons warm water (105-115 degrees)
3/4 cup milk
1/4 cup sugar
1/4 cup shortening
1 teaspoon salt
3 cups all-purpose flour
1 large egg
Combine yeast and warm water in a 1-cup liquid measuring cup, and let stand 5 minutes. Combine milk and next 3 ingredients in a saucepan; cook over low heat until shortening melts, stirring occasionally. Remove from heat, and cool to 105°-115 °. Combine yeast mixture, liquid mixture, 2 cups flour, and egg in a large mixing bowl; beat at medium speed with an electric mixer 2 minutes. Gradually stir in enough remaining flour to make a soft dough.
Turn dough out onto a lightly floured surface, and knead until smooth and elastic (8-10 minutes). Place in a well-greased bowl, turning to grease top. Cover and let rise in a warm place (85 degrees), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; turn out onto a floured surface. Roll dough into a 12 x 10" rectangle; cut into 2 inch squares. Place squares on a lightly floured surface; cover and let rise in a warm palce, free from drafts, 45 minutes or until doubled in bulk. Pour oil to depth of 3-4" into a large heavy skillet; heat to 375 °. Fry beignets, 4 at a time, in hot oil 1 minute on each side or until golden. Drain on paper towels; sprinkle with powdered sugar.