Add all the ingredients in the order suggested by your bread machine. Set your bread machine for the dough cycle, and let the machine run that full cycle.
When the dough is ready, divide it into 3 sections and braid it and place it on a parchment covered baking sheet. Cover it with plastic wrap and let it rise 20 minutes.
Brush it all over with the egg wash and bake it at 375° for 25 minutes.