Set a large shallow roasting pan of water on the lowest rack of the oven. Preheat oven to 400F, with a rack in center of the oven, as well.
When homemade buns have doubled, beat remaining egg with 1 tablespoon water and brush the buns thoroughly. * Be sure to brush the entire bun, top and sides, right down to the pan, as any areas you miss will be pale-coloured once baked.
If desired, you could sprinkle with sesame or poppy seeds at this point, as well. Bake, turning sheet 180 degrees halfway through baking, until tops are golden brown, about 15 minutes.
Immediately transfer your homemade buns to a rack to cool completely.
