• Mix the dough. Combine flour, salt, yeast, and milk powder in the bowl of a stand mixer fitted with a dough hook. In a separate bowl, whisk together warm milk, honey, egg, and egg yolk. Pour the wet ingredients into the dry ingredients. Mix on low speed (KitchenAid speed 2-3) until the dough comes together in a shaggy messy ball on the dough hook, about 3-5 minutes. 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.
If the dough hasn't reached windowpane stage after about 7 minutes, drizzle in an additional ½ teaspoon milk while kneading, then 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 running 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 it will come back together. Pause the mixer to gather the dough around the hook or scrape the butter down into the bowl occasionally as needed. This can take 10-15 minutes. Be patient!
If the butter chunks are struggling to incorporate, lightly dust in flour as the dough kneads — it will help the butter cling to the dough. Resist adding more flour unless absolutely needed!
• Knead the dough again. Continue kneading on medium speed until the dough is smooth, shiny, and passes the windowpane test again, about 5-7 minutes. Be patient!
• Cover and rise. Place the dough ball in a lightly greased bowl or container. Cover and let rise at room temperature (72°F) until just about doubled in size, about 1 hour. If not doubled after an hour, let it rise an additional 30-60 minutes until doubled.
Use the fingerprint test to check when the dough is ready to shape.

Assembly and Shaping

• Deflate the dough. Turn dough out onto a clean, lightly floured work surface. Use your hands to gently deflate the dough. Divide the dough into eight equal pieces using a kitchen scale (each piece should weigh about 88 grams).
If the dough is very sticky because its warm in your kitchen and the butter is melting, cover and pop the dough in the fridge for about 10-15 minutes or up to 1 hour before you start shaping. Cooling down the butter in the dough makes brioche easier to handle.
• Shape the hot dog buns. Gently flatten each piece of dough against the counter into a long rectangle shape, stacking any smaller pieces on top of larger pieces if you're combining them. Roll the top edge down, pressing with your fingertips to seal. Repeat this until the dough has formed a log, folding the two short sides in or tucking the top corners down as needed to even out the sides. Gently roll the log to even it out until it's about 7 inches long.

  Repeat with the remaining 7 pieces of dough, then arrange in a greased and parchment lined loaf pan in two rows of four.
Brioche dough is very pliable. If you need to nudge or squish in one thinner end or roll a thicker end a bit thinner to get an even 7-inch rope of dough, that's absolutely fine.
• Final Rise. Arrange the 8 hot dog buns on a parchment lined sheet pan with the seams tucked underneath. Spray the tops lightly with non-stick spray or brush lightly with oil. Cover with plastic wrap and let rise at room temperature for 1-2 hours or until doubled in size. They should look puffy and if you lightly press a finger into one, the indentation should fill in slowly and not all the way.

Baking

• During the last 30 minutes of the dough rising, preheat the oven to 350°F. Whisk together the leftover egg white and milk to make the egg wash.
• Egg wash and bake. Brush the top of the hot dog buns with the egg wash. Use a lame or sharp knife to lightly score lengthwise down the top of each bun. Bake for 14-16 minutes until golden brown on top and an internal temperature of at least 190°F.
Scoring the top helps create a vent for steam to escape as the hot dog buns bake. If you don't score the hot dog buns, the steam will look for the weakest point to use as a vent and will blow out the bottom of the buns where the seam is.
• Cool. Let cool slightly on the pan, then remove to a rack to finish cooling completely.