In a large bowl, dissolve yeast in warm water. Add the milk, shortening, sugar, salt, 3 eggs and 4 cups flour. Beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 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. Turn onto a lightly floured surface; divide in half. Divide each portion into thirds. Shape each piece into a 12-in. rope. Place three ropes on a greased baking pan; braid. Pinch ends to seal and tuck under. Repeat with remaining dough. Cover and let rise until doubled, about 45 minutes.
Beat remaining egg and cold water; brush over braids. Sprinkle with sesame seeds. Bake at 350° for 30-35 minutes or until golden brown. Remove from pans to wire racks to cool.