Make the dough:  In the bowl of your stand-up mixer with the dough hook attachment, add the flour, yeast, and salt.  Give them a quick stir.

In a small saucepan over medium-low heat, warm the milk, butter, and honey, until butter is melted.  Make sure it doesn't get too hot and scald the milk.  As soon as the butter is melted, remove from heat and set it aside to cool slightly (if it's too hot, the yeast won't rise).

In a small bowl, beat the egg and egg yolks.

Turn the mixer on low/medium (about a 3 to 4) and slowly pour the milk mixture into the dry ingredients.  Add in the beaten eggs in as well. 

Mix with the machine on medium speed (I'd stay at about a 4 or 5 speed out of 10) for 5 to 7 minutes, until smooth and elastic.  You may need to scrape down the sides and bottom of the bowl at first to get all the flour incorporated.  The dough will be soft and sticky and that's not only okay, it's what we want! 

Rub a medium bowl with about a teaspoon of olive oil and transfer the dough to the bowl. Cover with a clean kitchen towel or plastic wrap, and allow to rise for 30-40 minutes. Alternatively, cover with a lid or plastic wrap and allow to rise in the fridge for 12 to 24 hours (if you have the time, you get even more amazing flavor).

Shape the rolls:  Butter a 9×13-inch baking pan or something comparable and set aside.  Note, if you had the dough in the fridge, it will need time to come to room temp or will need a longer second rise!

Gently punch down the dough and divide it into 15 equal pieces.  If you want them to be the same exact size, you can weigh them out (each piece of dough should weigh ~64 grams).  I live on the edge.

See my shaping video in the post above...basically, you kind of smoosh it into a flat-ish circle, then stretch and pull the edges to the middle, pinching the dough together into a ball.  Then roll the pinched seam on the counter to get a smooth ball.

Transfer them to the buttered pan, leaving space in between for them to rise.  Cover loosely with plastic wrap or a kitchen towel and let them rise for about 1 to 1 1/2 hours.  They should double in size and be puffy and supple.

Bake the rolls:  Preheat the oven to 350 F.  Brush the tops of the rolls with the egg wash and transfer to the oven to bake until golden brown.  Start at 20-30 minutes, but it may need a tad more.  You want it to reach 200 F inside the middle of the rolls.  Honestly, I think mine could have used maybe 3 to 5 minutes extra and still not been overdone.

Glaze the rolls:  In a small saucepan, melt the butter and add the honey. Mix together until smooth.  When the buns come out of the oven, immediately brush the tops with the honey butter mixture and sprinkle with flaky sea salt.