Melt the butter in a saucepan on the stovetop. Add the milk and bring the temperature up to between 105℉ and 115℉ (41-46℃). Don't add it to the yeast mixture above 120℉ (49℃).
Whisk the dry ingredients together in the bowl of a stand mixer.
Add the warm milk, melted butter, and one egg. Run the machine with the dough hook, stopping to scrape down the sides a couple of times, until the flour mixture is all incorporated into the moist batter. Then, run the machine on second-to-low speed for about 5 minutes to knead the dough (6 to 8 minutes by hand). It should be soft and sticky.
Line a baking sheet with parchment paper.
On a floured surface, divide the dough into 8 equal sections. Roll each section between floured hands to shape nice, smooth balls for the buns. Place each one, with space between, on the prepared baking sheet.
Cover the buns loosely with plastic wrap and allow them to rise in a warm place. 75℉ to 85℉ (24-30℃) is ideal. This should take about one hour to one hour and fifteen minutes, or until the volume of the dough has increased by 50%. If the air is cooler, it may take a little longer.
Preheat the oven to 400℉ (204℃). Meanwhile, whisk a tablespoon of water into the second egg. Brush some of it carefully over the risen buns and sprinkle them with sesame seeds.
Bake the buns in a preheated oven for 15-20 minutes.
Cool on a wire rack before slicing.
Notes
Weigh your ingredients rather than measuring in cups. Weighing is much more accurate, and you'll get better results.
Proof your buns on the same baking sheet that you'll use for baking them. You want to avoid handling the dough and knocking any air out after it has risen, but before baking.