Whisk dry yeast, 30 grams of flour and the warm water into a bowl.
Let stand until mixture is foamy (should be 15 minutes).
Beat the egg with a whisk and split it into two equal halves. Set one half aside to coat the buns later.
Mix one half of the beaten egg with the melted butter, sugar and salt into the yeast mixture, then add the remaining flour (195g).
Knead the dough until soft and sticky, 5 to 6 minutes. You want a sticky, tacky dough, but not so sticky that big chunks stay attached to your spatula or fingers, so add flour or water if necessary.
Form the dough into a smooth, round shape, tucking loose ends underneath.
Coat a clean bowl with a drizzle of olive oil, set the dough ball in and rotate it a few times to cover it with a thin amount of oil. Cover the bowl with aluminum foil, then let rise in a warm place for about 2 hours (the dough volume should double).
Transfer the dough back to a lightly floured surface. (You don't want to use too much flour!) Pat it to flatten the air bubbles, then form into a shape, 1 to 2 cm thick, that you can easily cut into 4 equal pieces.
Form each piece into a round shape, very gently tucking loose ends underneath. Then pat and stretch them into flat discs 1 to 2 cm thick.
Arrange the buns on a baking sheet lined with parchment paper. Expect them to rise and double in volume, so space them enough. (You might want them to barely touch each other after rising, to get that typical hamburger bun look.)
Dust very lightly with flour then drape with plastic wrap. (No tight seal!) Let buns rise for about 1 more hour (they should double in volume again).
Preheat oven to 190C.
Mix thoroughly milk with the other half beaten egg. Using a brush, apply the egg wash very gently to lightly coat the top of the buns.
Be careful not to deflate the risen dough!
Sprinkle with sesame seeds.
Bake in the preheated oven until lightly browned on top (should be 15 to 17 minutes). Let cool completely before tearing apart, slicing in halves and making burgers!
Time to make burgers!
