In a bowl of a stand mixer, combine yeast, water and 1 tablespoons 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 remaining tablespoons honey; set aside.
After the yeast is alive and foamy, pour in the egg mixture and mostly all 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 tablespoons of flour mixture until the dough releases from the sides of the bowl. To know when it’s done, the texture should be soft, slightly sticking but not enough to stick on fingers and when pressing down on it, the dough bounces it back.
Transfer dough to a lightly floured work surface and form a ball by pulling dough under. Place in a large bowl lightly oil and roll the dough around to coat it with oil as well. Place a clean light dish towel and place the bowl in a draft-free area such as inside the oven (with temperature off) and let it rise for 2 hours or until it double in size.
Transfer dough back to floured work surface and knead for a couple minutes. Stretch dough into a rounded rectangular shape of 1 foot long by 5-inched wide. Using a bench scrapper, cut it in half then each half in half and finally half again. This recipe makes 8 large hamburger buns but if prefer, it can always be cut in smaller pieces.
Form a small ball with each piece by pulling dough under. Gently stretch each of them into a flat disc of ½-inch thick and place them onto a large baking sheet lined with silicone mat or parchment paper. Cover them with the same light dish towel and place it back to the oven (temperature off) for a second rise of 1 hour. Make sure the towel is NOT tucked under and place loosely on top otherwise the buns won’t rise.
When time is up, gently remove them from the oven and preheat it to 375ºF. Remove gently the towel and delicately brush an egg wash on each bun – be gentle otherwise they might deflate. Sprinkle sesame seeds over and transfer to preheated oven. Bake for 17 minutes or until golden brown.
Remove from the heat and let buns cool off completely before separating them and then slicing them in half crosswise for the burgers.