In a large bowl, dissolve yeast in warm milk. Add the sugar, applesauce, egg whites, salt and 2 cups flour; beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a lightly floured surface; knead until smooth and elastic, 6-8 minutes (dough will be slightly sticky). Place in a bowl coated with cooking spray, turning once to coat top. Cover and let rise in a warm place until doubled, about 1 hour.
Turn dough onto a lightly floured surface; divide into 24 pieces. Shape each portion into an 8-in. rope; tie into a knot. Place on 2 baking sheets coated with cooking spray.
Cover and let rise until doubled, about 30 minutes.Bake at 375° until golden brown, 12-16 minutes. Remove from pans to wire racks to cool.