In large bowl, combine 1 cup flour, sugar, salt and yeast; mix well. In small saucepan, heat 1 cup 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. Stir in an additional 1 1/2 to 1 3/4 cups flour until dough pulls cleanly away from sides of bowl.
On floured surface, knead in 1/2 to 3/4 cup flour until dough is smooth and elastic, about 5 minutes. Place dough in greased bowl; cover loosely with greased plastic wrap and cloth towel. Let rise in warm place (80 to 85°F.) until light and doubled in size, 45 to 60 minutes.
Grease cookie sheets. Punch down dough several times to remove all air bubbles. Shape dough into ball. Divide dough into 12 pieces. Roll each into 16-inch rope; form each rope into pretzel shape. Place on greased cookie sheets. Cover; let rise in warm place until light, 15 to 20 minutes.
Heat oven to 400°F. In large nonaluminum saucepan, combine 6 cups water and baking soda; mix well. Bring to a boil. Drop pretzels, one at a time, into water that is just boiling; cook 5 seconds on each side. Remove pretzels from water with slotted spoon; place on greased cookie sheet. In small bowl, combine 1 tablespoon water and egg white; beat well. Brush over pretzels. Sprinkle with coarse salt.
Bake at 400°F. for 8 to 10 minutes or until golden brown. Immediately remove from cookie sheets; cool on wire racks for 5 minutes. Serve warm.