In a bowl, combine 2 cups flour, soup mix, yeast, sugar and salt; add warm water and shortening. Beat on medium speed for 3 minutes.
Add enough remaining flour to form a soft dough. Turn onto a floured surface; knead until smooth and elastic, about 3 minutes.
Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour. Punch dough down; knead 4-5 times. Divide in half.
Roll each portion into a 14-in. x 6-in. rectangle.
Roll up, jelly-roll style, starting with a long side; pinch edges and ends to seal.
Place seam side down on a greased baking sheet. Beat egg white and water; brush over loaves. Cover with plastic wrap that has been sprayed with cooking spray; let rise until doubled, about 30-40 minutes. With a sharp knife, make four shallow diagonal cuts across the top.
Bake at 375° for 30-35 minutes or until golden brown. Cool on a wire rack.