Microwave 1 1/2 cups milk at HIGH in a microwave-safe glass bowl 2 to 3 minutes or until heated. Stir in yeast; let stand 5 minutes.
Combine 5 1/2 cups flour and salt in a large bowl; stir in yeast mixture. Add shortening and next 3 ingredients. Beat at low speed with an electric mixer 1 to 2 minutes. Beat at medium speed 5 more minutes.
Sprinkle dough with additional flour, and remove from bowl. (Dough will be very sticky.) Place dough in a lightly greased bowl, turning to grease top. Turn off oven. Cover bowl with plastic wrap, and let rise in oven 30 minutes or until doubled in bulk. Remove from oven. Remove and discard plastic wrap.
Punch dough down, and divide in half. Divide each half into 3 equal portions. Roll each portion into a 14-inch-long rope; pinch 3 ropes together at one end to seal, and braid. Repeat with remaining dough portions. Place braids on a parchment paper-lined baking sheet.
Cover braids with plastic wrap, and let rise in a warm place, free from drafts, 25 to 30 minutes or until doubled in bulk. Brush evenly with beaten egg, and sprinkle with sesame seeds, if desired.
Bake at 350° for 25 minutes or until golden. (A wooden pick should come out clean.)