• Mix the dough. Combine flour, salt, and yeast in the bowl of a stand mixer fitted with a dough hook. In a separate bowl, whisk warm milk, honey, and egg. Pour the wet ingredients into the dry ingredients. Mix on low speed until the dough comes together in a shaggy messy ball on the dough hook. The dough will look dry at first, but will hydrate as it mixes. Be patient!
• Knead the dough. Increase speed to medium and knead until the dough passes the windowpane test, about 7-10 minutes. Dust in more flour or drizzle in more milk ¼ teaspoon at a time only as needed. If the dough hasn't reached windowpane after about 10 minutes, cover and rest for 5-10 minutes. Knead 2-3 minutes more. It should get there!
If you don't reach a perfect windowpane before adding the butter and it's been at least 10 minutes of kneading, you can go ahead and start adding butter. It won't be a technically perfect brioche, but it will still be delicious!
• Add the butter 1 tablespoon at a time. With the mixer on medium, add the butter one tablespoon at a time. Let each piece fully incorporate before adding more. The dough will look like it is falling apart each time you add more butter, but will come back together. If the butter chunks are struggling to incorporate, lightly dust in ¼ teaspoon of flour — it will help the butter cling to the dough. Resist adding more flour unless absolutely needed!
• Knead the dough again. Increase speed to medium-high and knead until the dough is smooth, shiny, and passes the windowpane test again, about 5-10 minutes.
• Cover and rise. Place the dough ball in a lightly greased bowl or container. Cover and let rise 1 hour at room temperature (72-75°F) until just about doubled in size. If not doubled after an hour, let it rise an additional 30-60 minutes until doubled. When you push a finger into it, the indentation should fill back slowly and incompletely.
Due to the extra weight of the butter on the gluten network, don't worry if your dough needs up to an extra hour of time to rise, especially if your kitchen is cold. It's more important that the dough looks and feels right than that a certain amount of time has passed. If the dough needs another 30 or even 60 minutes to rise, that's fine.

Assembly and Shaping

• Divide the dough. Turn dough out onto a clean, lightly floured work surface. Divide it into six equal pieces using a kitchen scale (each piece should weigh about 110 grams).
The butter in the brioche dough can make it sticky and harder to handle. If you feel like it's clinging and the butter is melting and sticking to you, pop it in the fridge for 10-15 minutes to help the butter firm up before shaping.
• Shape the burger buns. Gently flatten each piece of dough against a clean, unfloured counter, stacking any smaller pieces on top of larger pieces if you're combining them. Fold or tuck the edges up across the middle of the dough to create a ball, then pinch the edges together to create tension and a smooth round top on the other side of the dough. Place the dough down with the smooth side up and the pinched-together seam against the counter. Cup your hand around it with your pinkie against the counter and scoot it in circles to tighten the seam and further tighten up the top.

  Repeat with the remaining five pieces of dough, then cover with a clean towel and rest for 10 minutes.
• Tighten. Give each brioche bun another scoot in circles on the counter to tighten them up and make sure all the edges are tucked underneath, then place on a parchment lined sheet pan with plenty of room to spread out.
• Final Rise. Lightly brush with oil or spray the tops of the buns with non-stick spray, then cover with plastic wrap. Place a second sheet pan on top of the shaped buns to weigh them down. Cover and let rise at room temperature for 1-2 hours or until the dough balls have doubled in size and are looking quite airy and spring back when you poke them.
Don't press down on the sheet pan, you don't want to force the dough to expand faster than it's ready to. The weight of the sheet pan alone is enough to nudge the dough to expand outward during its final rise.

Baking

• During the last 30 minutes of the final rise, preheat the oven to 350°F. Whisk together egg and milk to make the egg wash.
• Egg wash and bake. Brush the tops and sides of the buns lightly with egg wash and sprinkle with sesame seeds (if using). Use a sharp knife or lame to cut a shallow X in the top of each bun. Bake for 17-20 minutes until golden brown on top and an internal temperature of at least 190°F.
• Cool. Let cool for a few minutes on the pan, then remove to a rack to finish cooling completely. If you slice the buns while they're hot, the steam still trapped inside them will turn the starches into mush.