Combine water, flour, sugar, salt, yeast, egg, andthe butter in a large bowl. Knead to form a soft, smooth dough.
Cover dough and let rise until nearly doubled.
Deflate the dough and divide in to eight pieces, forming each into a ball. Flatten each ball into a 3 inch disk and place on a parchment-lined baking sheet.
Cover buns and let rise until noticeably puffy. Just before finished rising, preheat the oven to 375.F.
Whisk together the egg white and cool water. Brush the buns gently with the egg wash.
Bake buns until golden brown. Cool buns on a rack
Made a batch, but tried to shape into hotdog buns by rolling into cylinders and baking in a rectangular dish. This worked alright, but the dish wasn't long enough for all 8, resulting in too tall, narrow buns. When forming the cylinders, stretch the portions of dough into an oblong shape before rolling into a cylinder.
Made again without needing to add additional water; used active dry yeast without proofing first; did not wash before baking. When rolling, I found that if I exerted too much pressure on them, the balls became overly sticky and the surface lost the nice smooth texture. Next time I will take care to roll just enough to form into a ball.
Made using only 170g water and no wash at all. Used active dry yeast instead of instant and let proof 10 minutes in the water and sugar. After the first proof, the dough was nearly tripped in size. These are very nice and very easy. I will continue using this for burger buns, and may even try dividing this dough into smaller portions to make dinner rolls.
Made a second batch in an attempt to create hotdog buns, with slightly better success. I divided the dough into two batches to give them more space in the pan I have, which unfortunately was a bit too much space, as they didn't rice enough to press against each other, resulting in rather irregularly shaped buns.