Add milk to a small saucepan and heat over medium-high heat until warmed to 90°F to 100°F, and remove from heat. Add active dry yeast, stirring to combine. Allow to bloom 5 to 10-minutes until active and frothy.

While yeast mixture rests, add the fine sea salt and bread flour in the bowl of a stand mixer and whisk to combine. Add the yeast mixture and beaten eggs to the dry ingredients and knead on low speed until combined, approximately 5 minutes. Scrape down the sides of the bowl as needed.

Once you have a rough dough, increase the speed to medium-low and add the softened unsalted butter one tablespoon at a time until thoroughly combined and the dough is smooth, about 5 to 7 minutes.

Turn the dough out onto an floured work surface and shape into a smooth ball. Place dough into a large mixing bowl, cover and rest for 1-hour until doubled in size. Towards the end of the first rise, line a baking sheet with parchment paper and set aside. Once the dough has risen, turn it out onto a floured work surface and punch it down.

Divide the dough into 12 equal pieces, about 45 grams each. Form each piece of dough in to a ball, tucking the edges together and then pinching the seams together on the bottom. Using the friction of the work surface, use a scooping motion to roll them into tight dough balls.

Transfer the dough balls on a parchment paper-lined baking sheet, and gently press the tops down to lightly flatten. Cover with a damp kitchen towel and proof 1 to 2 more hour(s) - 2 hours preferred.

Towards the end of the second proof, preheat the oven to 375*F.

In a small container, combine the remaining egg and 1 tablespoon of whole milk. Brush the egg wash over the tops of the buns. Optionally top with sesame seeds, poppy sees, or flaky sea salt.

Transfer to the oven and bake for 20 to 25 minutes until golden brown and shiny. Remove from the oven and transfer to a wire cooling rack until cooled completely.