Blend the flour, sugar and salt in a mixing bowl. Add the butter, yeast mixture and milk, and mix by hand to form a dough. Knead five minutes with an electric mixer with dough hook, or turn the dough out onto a lightly floured surface and knead for seven to nine minutes by hand.
As the dough kneads, add small amounts of additional flour or warm water as necessary to achieve a dough that is light and slightly sticky.
When the dough has been kneaded until smooth, transfer it to a greased bowl and turn over the dough once to coat it with oil. Cover the bowl with a towel, and leave the hamburger roll dough to rise until doubled in bulk, about one to one-and-a-half hours.
Turn the dough out of the bowl and divide it into 12 portions. Shape each portion into a smooth ball and place the dough on a greased baking sheet. Lightly pat the tops of the balls of dough to flatten them slightly.
Cover the tray with a towel, and leave the dough to rise again for another hour to hour-and-a-half.
Preheat an oven to 425° F. If garnishing the hamburger buns with sesame seeds, brush the rolls with the egg wash and sprinkle sesame seeds on top. Bake the hamburger rolls until rich golden brown, about 20 minutes. Immediately upon removing the rolls from the oven, brush their tops lightly with melted butter or vegetable oil.
Transfer the sandwich rolls to a rack and cover them loosely with a towel to trap steam and keep the crust soft as they cool. Store thoroughly cooled rolls in a plastic container or plastic ziploc bag. Freeze any rolls which won't be used within a day.