To make the dough: Combine all dough ingredients except for the butter in the bowl of a stand mixer. Mix on low speed for a minute or two until the flour is all absorbed, then mix on high or medium high speed for about 10 minutes until you have a soft, smooth dough that is close to passing the windowpane test.

Add the softened butter and mix for a few more minutes until all combined. The dough should be smooth, strong, and slightly shiny. Shape it into a ball in the mixing bowl and cover. Let rise until it's nearly doubled in size, about 1 to 2 hours.

To shape the buns: Gently deflate the dough and divide into 15-24 rolls depending on the size you want. For extra large rolls (about 105g each), make 15 rolls. For standard size, measure each roll out to about 63g (this will make 24 rolls). Shape each piece into a ball. Place buns on a lightly greased parchment-lined baking sheet. Cover and let rise until light and puffy, about 1 hour to 1.5 hours. Toward the end of the rising time, preheat the oven to 375°F.

Make the egg wash: Mix one egg with a splash of milk or cream (or a splash of cream with a small splash of water). Brush over the buns before baking. Sprinkle with coarse sea salt if desired.

To bake the buns: If the buns are small, bake for about 16-18 minutes, until golden. For large buns around 100g, bake for about 25 minutes, or until the middle of a roll reads 190F on a thermometer. For XL ones, you can take them out when a roll in the center of the pan is getting close to 185F since it will continue to cook a little bit once you take it out.

Optional: Once they're out of the oven, brush with melted butter or rub a cold stick of butter over the top of the rolls and it will melt onto them. This will give them a satiny, buttery crust.

Storage: For same-day storage, cover/wrap in a clean kitchen towel or put them in a paper bag or ziplock bag without zipping. If saving for the next day or two, store leftover buns well-wrapped at room temperature for several days; freeze for longer storage.