Using the bowl of your stand mixer, whisk together the yeast, milk, 1 egg, and 1 cup of flour. Sprinkle the second cup of flour over the mixture, covering it (do not incorporate). Let the sponge rest for 30 minutes. At this point, check the sponge – if there are cracks and craters across the top layer of flour, you know your yeast is doing its job!

Turn the top layer of flour into the sponge with a spatula, and then add the sugar and salt. Using the dough hook with your mixer on medium-low speed, work in the eggs individually, and then 1 more cup flour. Increase the speed of your mixer to full incorporate, then add the remaining ½ cup flour.

Once all the flour is worked into the dough, increase the speed to medium and allow the dough to mix for 5 minutes undisturbed (no less). The dough should be sticky and very pliable, but if too wet, add another ¼ cup flour.

Once the dough has come together, start adding the cubes of butter a few at a time, adding more as they become incorporated. Mix on medium low for another 5 minutes.

Transfer the ball of dough to a large bowl greased with butter and let it sit for 2 hours at room temperature until it doubles in size.

Using a spatula, flip the ball of dough over in the bowl and cover it with plastic wrap. Let it rise for 6-8 hours more (or overnight).

Heat the oven to 375 degrees F and grease an oven safe casserole dish with butter (you can also line two baking sheets with parchment paper).

Dump the dough out onto a lightly floured surface. Divide the dough in quarters and then each quarter into thirds, so that you have 12 total balls of dough. Arrange the balls of dough in the prepared dish, about 1 inch apart. The buns will expand into eachother as they bake, allowing them to be nice and soft when you pull them apart later. Cover the dish with plastic wrap and let the dough rise one last time for 30 minutes.

Whisk together the egg yolk and milk in a small bowl. Brush the brioche buns with the egg wash and sprinkle with sesame seeds, poppy seeds, and/or sea salt, as desired. Bake for 15-20 minutes, until the buns are beautifully golden and round.

Let the brioche buns cool in the pan before taking them apart. Use right away, or store in an airtight container at room temperature for up to 3 days.

To freeze, let the brioche buns cool completely, lay the individual buns out on a baking sheet lined with parchment paper, and freeze for at least an hour. Transfer the frozen rolls to a freezer-safe bag and use within 6 months.