In the bowl of the stand mixer, pour the flour, sugar, and dry yeast. If using fresh yeast, dissolve it first in lukewarm milk.
Add the slightly warmed milk, then knead for 3 minutes on low speed.
Gradually incorporate the soft butter.
As soon as the butter is added, increase the speed to 2 and knead for 3 minutes.
Add the whole egg and continue kneading for 3 minutes at speed 2.
Finish by adding the salt, then knead for another 3 minutes.
Total kneading time: approximately 12 minutes (3 minutes on low speed, then 9 minutes at speed 2).
The dough should be soft, smooth, and pull away from the sides of the bowl, forming a beautiful, homogeneous ball.
Gather the dough into a ball and let it rise in the stand mixer bowl or transfer it to a large, lightly oiled bowl. Cover with plastic wrap, then place a towel over it.
Let rise for 1 hour 30 minutes to 2 hours, until the dough has doubled or even tripled in volume.
Once the dough has risen, degas it by pressing down firmly with your fist until it loses all its volume.
Weigh the dough and divide it into 10 equal portions. I got balls weighing about 90 g each.
Shape each piece into a smooth, round ball.
Place them on a baking sheet lined with parchment paper, spacing them well apart as they will expand during proofing.
Cover the baking sheet with a clean towel and let the dough rise for about an hour (or longer if needed). The balls should puff up nicely.
When proofing is complete, preheat the oven to 170 °C (340 °F).
Gently brush the dough balls with an egg yolk mixed with a few drops of milk. Use a soft brush to avoid flattening them.
Sprinkle the buns with sesame seeds or a mixed seed blend.
Bake for about 15 minutes, until the burger buns are golden brown.
Place them on a wire rack as soon as they come out of the oven, then cover them with a clean towel to retain their moisture and softness.