Add the yeast, milk and sugar to the bowl of your stand mixer fitted with the dough hook attachment (or if making by hand, to a large mixing bowl). Mix with a fork and let sit for 3-5 minutes until bubbly.
Add the egg and melted butter and mix well.
Add the flour and salt and mix on low speed with the dough hook until a soft dough forms.
Continue the mixer on low speed, turning up to medium-low speed until the dough pulls away from the sides of the bowl. The dough will be soft and a little bit sticky or tacky.
If making the dough by hand, turn it out onto a lightly floured surface and knead for about 4-5 minutes until a soft and sticky dough forms.
Shape the dough into a ball and place it in the mixing bowl. Place the mixing bowl inside another larger mixing bowl and pour hot water into the larger bowl so the mixing bowl containing the dough is sitting in the water. Be careful not to get any water into the bowl with the dough, and only use hot water, not boiling water as it may cook the dough.
Cover the bowls with a clean kitchen towel and let the dough rise for about 15-20 minutes.
After the dough has risen, punch the dough down and turn it out onto a lightly oiled surface. Give the dough a quick knead and form it into a large ball.
Weigh the ball of dough and divide the total weight by 24. Begin portioning out the dough according to the weight to create 24 equally-weighted pieces. If you aren't using a kitchen scale, use a sharp knife cut the dough in half, then in half again, and then cut each of those pieces into 5 equally sized pieces, making sure the pieces of dough are as close to the same size as possible.
Roll each piece into a round ball, rolling the ball in a circular motion against the work surface to create surface tension. Place on a greased baking sheet (line the baking sheet with parchment paper if desired).
Brush the buns with the egg wash and sprinkle with some salt, if desired.
Set your oven to 375 degrees Fahrenheit and add the pan with the buns to the cold oven. They'll complete the second rise in the oven as it preheats. When you add the buns to the oven, set the timer for 20 minutes.
Once the timer goes off, check the buns. If they need a few more minutes, continue baking for up to 3-5 minutes more until the buns are golden brown on top.