In large bowl, combine 3 cups flour, sugar, salt and yeast, mix well. In small saucepan, heat 2 cups water and shortening until very warm (120 to 130 F.). Add warm liquid to flour mixture, blend at low speed until moistened. Beat 3 minutes at medium speed. By hand, stir in an additional 1 1/2 to 2 1/4 cups flour to form a stiff dough.
On floured surface, knead in 1/4 to 1/2 cup flour until dough is smooth and elastic, about 8 minutes. Place dough in greased bowl, cover loosely with greased plastic warp and cloth towel. Let rise in warm place (80 to 85 F.) until light and doubled in size, 45 to 60 minutes.
Grease large cookie sheet. Punch down dough several times to remove all air bubbles. Divide dough in half, divide each half into 3 equal parts. Roll each part into 14-inch rope. Braid 3 ropes together, seal ends. Place on greased cookie sheet. Repeat with other half of dough.
In small bowl, combine 1 tablespoon and egg white, beat sightly. Carefully brush over loaves. Cover, let rise in warm place until light and doubled in size, 20 to 30 minutes.
Heat oven to 375 F. Uncover dough, brush loaves again with egg white mixture. Bake at 375 F. for 25 to 30 minutes or until golden brown. Immediately remove from cookie sheet, cool on wire racks for 1 hour or until completely cooled.