• 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!
• 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.

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).
• Shape the burger buns. Gently flatten each piece of dough against the 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 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 on 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 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.

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.

Storage & Freezing

• You can store your homemade brioche burger buns in an airtight bag with as much air pressed out of it as possible for 5-7 days at room temperature. They will be at their softest on the same day you bake them and will become firmer over time.

  To freeze, I usually slice the buns almost all the way through first so they stay together but are still easy to separate, though you can freeze them whole if you prefer.

  To toast up the frozen sliced buns, separate the two frozen halves and pop them in a 350°F oven for about 4-5 minutes. To simply defrost and warm up the burger buns, leave them in the bag on the counter for about an hour, then warm them up in a 250°F oven for about 10-15 minutes.