In the bowl of a stand mixer, combine yeast, water and 1 tbsp. honey; stir and let it sit for 15 minutes or until foamy. Meanwhile, in a medium bowl, combine all-purpose flour, bread flour and sea salt; whisk until very well blended.
In another bowl, beat 1 egg with melted butter and the remaining 1 tbsp. honey; set aside. After the yeast is alive and foamy, pour in the egg mixture and most of the dry ingredients, keeping about ½ cup on the side.
With the dough hook attachment, process on speed 2 for 2 minutes. Increase the speed to 3 and add 1 tbsp. of flour mixture until the dough releases from the sides of the bowl and clings around the hook. To know when it’s done, the texture should be soft, slightly sticky but not enough to stick to the fingers and when pressing down on it, the dough bounces back.
Transfer the dough to a lightly floured work surface and form a ball by pulling it under. Place it in a large lightly oiled bowl and swirl it around to coat with oil. Cover the bowl with a clean light dish towel and place it in a draft-free area such as the oven (temperature off). Let it rise 2 hours or until it doubles in size.
Line a baking sheet with a silicone mat or parchment paper; set aside.
Later, punch the dough to deflate and transfer it back to the floured work surface; knead for a couple minutes.
Stretch the dough into an even rounded rectangular shape of 1 foot long by 5-inches wide. Using a bench scrapper, cut in half then each half in half and finally half again width-wise. This recipe makes 8 large hamburger buns but, it can always be cut into smaller pieces.
Form a small ball with each piece by pulling the dough under. Gently stretch each of them into a flat disc about ½-inch thick and place them on the prepared baking sheet.
Cover with the same light dish towel and place it back in the draft-free spot to proof for 1 hour. Make sure the towel is NOT tucked under and loosely placed on top otherwise the buns won’t rise.
When time is up, gently remove them from their draft-free spot.
Preheat the oven to 375ºF.
Gently remove the towel and delicately brush an egg wash on each bun – be gentle otherwise they might deflate.
Sprinkle on some sesame seeds and transfer to the preheated oven. Bake 17 minutes or until golden brown.
Remove from the heat and let the buns cool off completely before separating them and then slicing them in half crosswise for the burgers.