In a large bowl, combine the water, oil, sugar, and yeast. Let sit until the yeast is bubbly, about 8 minutes. Stir in the beaten egg, softened butter, and salt.
With a stand mixer or by hand, add the flour a cup at a time until you have a soft dough that is not sticky. Knead by hand 10 minutes, or 5 minutes with a stand mixer.
Divide the dough into 15 to 18 pieces and form into balls. Place in a greased 9x13 pan and cover with parchment paper and a kitchen towel. Let rise 10 minutes in a warm place (or up to 30 minutes).
Lightly brush with milk if desired and bake on the middle rack for 10-12 minutes, or just until browned.
Notes
I have even used half whole wheat and half all purpose flour.
The original directions call for salt, but the ingredient list has no salt amount.