Mix together milk, salt, butter and applesauce; set aside. Measure the warm water into a large bowl; sprinkle in yeast. Stir until dissolved. Stir in lukewarm milk mixture and half the flour. Add cinnamon; beat until smooth. Stir in enough remaining flour to make a soft dough. Turn out onto a lightly floured board. Knead until smooth and elastic about 8 minutes. Place in greased bowl, turning to grease top. Cover; let rise in warm place, free from drafts, until double in bulk, about 1 hour. Punch down dough, turn onto lightly floured board. Divide dough in half. Shape into 2 loaves, about 8 inches long. Place loaves on a greased baking sheet. Cover; let rise in warm place, free from drafts, until double in bulk, about 1 hour. While bread is rising, preheat oven to 375 degrees. Bake 25 minutes. Remove from oven and brush with egg white mixed with cold water. Return to oven, bake 5 minutes longer.