Mix all the dough ingredients with mixer, or bread machine to a soft, smooth dough.
Cover the dough, and let it rise for 1 to 2 hours, or until it's nearly doubled in bulk.
For bread machine
If using bread machine use and follow macines basic instructions and dough cycle.
Recipe final steps
Remove dough, and divide it into 8 pieces. Roll each piece into a round ball and flatten to about 3" across. Place the buns on a lightly greased large baking sheet, cover with hand towel, and let rise for about an hour, until noticeably puffy.
Brush egg wash or melted butter over top of dough.
Bake the buns in a preheated 375°F oven for 15 to 18 minutes, until golden. Remove them from the oven.
Brush with the remaining melted butter if using. Do not rebrush if using egg wash.
Cool the buns on a rack.
The following mixtures for a wash gives an idea for the look and taste you want:
Whole Egg + Milk Darker color, Shine
Whole Egg + Water Soft Crust, Shine, darker color
Egg Yolk + Milk or Cream Soft Crust, Shine, darker color
Egg White + Water Firm Crust, Shine
Milk / Cream Low shine, nice browning and a flakey appearance
Butter Smooth top, light and golden shiny and a rich flavor
Total cook time may vary upon the dough rising which relies on many variables.