Set a large shallow pan of water on the lowest rack in your oven. Preheat oven to 400 degrees with a rack in center. Beat remaining egg with one tablespoon water and lightly brush it on top of the buns. Sprinkle with sesame seeds, if using. Bake, turning sheet halfway through baking, until tops are golden brown, about 15 minutes. Transfer to a rack to cool completely. Serve around these burgers.