Using a Stand Mixer: (This can also be mixed with a spoon and kneaded by hand.)
In the mixer bowl, sprinkle 1 package yeast over 2 cups warm water (110-115°F) and 1/4 cup honey; let stand for 5 minutes to soften and bloom yeast. While yeast rests, prep a bowl or proofing tub with a little oil for the dough in step 4 by spreading the oil in a thin layer inside the bowl.
Using the paddle attachment, mix in 2 tablespoons butter, 1 whole egg, 1 egg yolk (reserve egg white), and 2 1/2 cups of the flour on medium-low speed until smooth. Drape with a towel and let dough rest for 20 minutes.
Add 2 teaspoons sea salt and enough of the remaining flour (1/2 cup at a time), mixing 1 minute after each add, to form a soft, shaggy dough (up to 5 1/2 cups total - humidity can affect the amount of flour it will take). Once the dough holds it's shape (though sticky) and is stable on the mixing paddle, spread 1/4 cup of flour out on the counter and sprinkle on dough. (See recipe video for demo.) With floured hands, knead dough by folding over and turning 4 or 5 times to form a soft ball that holds its shape and no longer slumps. Scrape any remaining flour from the counter and spread 1 tablespoon of oil on the counter. Leave the dough to rest on the counter and cover with a bowl for 5 minutes. With oiled hands, fold the dough 4 or 5 times again, and cover with the bowl to rest again for 5 minutes. Repeat one more time so the dough has 3 folding processes and 3 rests of 5 minutes each. This process allows the flour to fully hydrate. TIP: Because the dough can be tacky, use a pastry knife to help the dough release from the counter rather than adding more flour, which will make the dough heavy.
While you shouldn't need to, at this point, if the dough is still is not holding its shape and is too wet to handle, add 2-3 tablespoons more flour and complete the folding process again with an additional 5 minute rest. Otherwise, after the three folding/resting cycles, if the dough is forming a soft ball and is manageable with oiled hands, place the dough in an oiled bowl, turning over so the oiled surface it face-up.
Cover the bowl with plastic wrap and then a towel and let it rise in a warm spot (above 70°) for about 1 1/2 hours, or until nearly doubled in bulk. (The oven, with the oven light ON is a good place to let the dough rise if the room is cool.)
Once the dough forms a soft ball, oil a bowl with olive oil, place dough in bowl and turn over so that oiled surface is face-up.
Cover the bowl with plastic wrap and then a towel, and let it rise in a warm spot (above 70°) for 1 hour, or until nearly doubled. (The oven, with the oven light ON is a good place to let the dough rise if the room is cool.)
With oiled hands, punch down dough and divide it into 32 pieces on a lightly oiled surface (It is ideal to use a kitchen scale to measure the dough and then divide by 32 for the ideal weight of even bun). Shape each piece into a round, smooth ball, place on a parchment-lined baking sheet, and flatten with the palm of the hand to about 2-inches across (it helps to have oil on your hands when flattening the buns). It is best if the sides of the buns touch when flattened. Cover with a lightweight smooth towel, tented aluminum foil, or inverted rimmed baking sheet if the room is drafty. Let rise about 40 minutes, or almost doubled in size. (Because the dough can be tacky, avoid covering with terry cloth or microfiber cloth towels, which can "grab" the top of the dough.)
Just before placing in the oven, brush the buns gently with the beaten egg white on all exposed sides, sprinkle with sesame seeds. Alternatively, brush with melted butter once the are baked and removed from the oven for soft, matte finish.
Bake the buns at 375°F until golden in color 16-18 minutes, or until the interior registers 190°F using an instant-read thermometer. Cool the buns on the pan on a wire rack for 10 minutes, then remove from pan and cool completely on the wire rack. Slice once completely cooled.
The egg wash helps the seeds to stick and give the buns a shiny crust. Brush with melted butter for a soft, matte finish. The weather and type of flour can have an impact on the feel of the dough and how tacky it feels. Avoid adding a lot of extra flour to the dough to make it more manageable. Instead, use a pastry knife to scrape and lift it when kneading or switch to an oiled surface and oil for your hands to manage the dough. Buns can be made in advance and frozen for up to 3 months.