"I've gotten a thousand request for these. We're going to make our own, and not only are these going to be the perfect shape, they're going to taste way better than anything that comes out of a plastic bag. The total time takes almost 4 hours, but the actual amount of work involved is maybe 10 minutes."
Whisk 1 egg, melted butter, sugar, and salt thoroughly into yeast mixture. Add remaining flour (about 3 cups).
Fit a dough hook onto stand mixer and knead the dough on low speed until soft and sticky, 5 to 6 minutes. Scrape sides if needed. Poke and prod the dough with a silicone spatula; if large amounts of dough stick to the spatula, add a little more flour.
Wipe out stand mixer bowl, drizzle olive oil into the bowl, and turn dough over in the bowl several times to coat surface thinly with oil. Cover bowl with aluminum foil. Let dough rise in a warm place until doubled, about 2 hours.
Transfer dough to a floured work surface and pat to flatten bubbles and form into a slightly rounded rectangle of dough about 5x10 inches and about 1/2 inch thick. Dust dough lightly with flour if needed. Cut dough into 8 equal pieces. Form each piece into a round shape, gently tucking ends underneath as before.
Use your hands to gently pat and stretch the dough rounds into flat disc shapes about 1/2 inch thick. Arrange buns about 1/2 inch apart on prepared baking sheet. Dust buns very lightly with flour. Drape a piece of plastic wrap over the baking sheet (do not seal tightly). Let buns rise until doubled, about 1 hour.
Beat 1 egg with milk in a small bowl, using a fork, until mixture is thoroughly combined. Very gently and lightly brush tops of buns with egg wash without deflating the risen dough. Sprinkle each bun with sesame seeds.
Bake in the preheated oven until lightly browned on top, 15 to 17 minutes. Buns will stick together slightly where they touch. Let cool completely, tear the buns apart, and slice in half crosswise to serve.
One pound of flour is equal to about 3 1/2 cups.
When in doubt, go for dough that's a little too sticky rather than too dry. You can always knead a little more flour into these.