Line a baking sheet with a silicone mat or parchment paper.
Place the yeast in the bowl of a large stand mixer. Whisk in 1/2 cup flour and the warm water until smooth; let stand until foamy, 10 to 15 minutes.
Whisk 1 egg, melted butter, sugar, and salt into the yeast mixture. Add the remaining flour, about 3 cups.
Using a dough hook, knead on low speed until the dough is soft and sticky, 5 to 6 minutes, adding a little more flour if needed.
Transfer to a floured surface and form into a smooth round. Wipe out the mixer bowl, add the olive oil, and turn the dough to coat. Cover and let rise in a warm place until doubled, about 2 hours.
Transfer to a floured surface, flatten into a roughly 5-by-10-inch rectangle about 1/2 inch thick, and cut into 8 equal pieces. Form each into a round, then gently flatten into discs about 1/2 inch thick.
Arrange on the prepared baking sheet, cover loosely with plastic wrap, and let rise until doubled, about 1 hour.
Preheat the oven to 375°F (190°C). Beat the remaining egg with the milk and gently brush over the buns. Sprinkle with sesame seeds.
Bake until lightly browned, 15 to 17 minutes. Cool completely, separate the buns if necessary, and slice crosswise to serve.