In a stand mixer bowl, gently stir together yeast, warm milk, and sugar. Let sit for 10 minutes to bloom, if it doesn't foam up and smell yeasty, it is dead; you need to get living yeast and try again.

Add melted butter, salt, and egg to the yeast mixture. Whisk together well, then add in about 3 ¼ cups (180 g) flour. With a dough hook attachment on medium speed, knead the dough for about 8 minutes. The dough will be soft and slightly sticky, not shaggy, and will spring back up when touched when it's ready.

Separate the dough into 8-10 balls (depending on how big you want them) and place onto a baking sheet lined with parchment paper. Cover with a clean kitchen towel and let rise in a warm, draft-free space for 15 minutes.

Preheat oven to 425 degrees F (220 degrees C). Whisk the egg yolk and tablespoon of milk together in a small bowl to create an egg wash. Brush the egg wash over the tops and sides of the buns. Sprinkle the top of the brioche buns with sesame seeds, if desired.

Bake for 10 to 12 minutes, until buns are golden brown.

These buns can be frozen for up to two months. Wrap individually in plastic wrap and in a freezer-safe zip-top bag.