Place the ingredients for the dough in your bread machine in the order recommended by the manufacturer. Run on dough, or leaven dough, setting.
Remove the dough from the pan and gently set it onto a lightly floured surface. Devide your dough into 10 equal portions for buns (14 for rolls). Shape each piece into a ball and cover with either a flour sack towel or plastic wrap. Allow to rest for 20 minutes.
Shape each dough into your desired bun shape, pulling it so that the tops tighten.
Place on a baking pan that is either lightly geased, or has a silicon baking mat. Allow to rize for 50-60 minutes, or until doubled in size.
Preheat oven to 350°F
Brush the tops with the egg wash and bake for 15-20 minutes, until tops are nicely browned.