In a microwave safe measuring cup, heat the milk to 100°F / 38°C. Whisk in the yeast and the sugar. Set aside until the mixture begins to foam. (~5 minutes)
While waiting, add the flour, salt, egg, and butter to the bowl of a stand mixer fitted with the dough hook attachment. When the yeast mixture begins to foam, add it in to the rest of the ingredients.
Knead the dough on low speed for 1 minute to allow the ingredients to come together. Increase the speed to medium-high and knead for an additional 10-20 minutes, or until the dough passes the windowpane test.* (This will happen after the dough has cleaned the sides and bottom of the bowl)
Once the dough is done kneading, butter the inside of the bowl, form the dough into a ball and place it back in the bowl. Then cover the mixing bowl with plastic wrap. At this point, you could set the dough in the fridge to rise overnight, or continue with completing the recipe in one day. If doing in one day, set the dough in a warm area and wait for it to double in size (~1 hour.)
Once the dough has doubled in size, punch it down to remove excess air, then transfer it to a clean, lightly floured surface.
Divide the dough into 6 equally sized pieces, and roll each tightly into a ball.
Line a baking tray with parchment paper, and evenly spread the buns out on top of it. Cover the tray loosely with a towel.
Allow the buns to rise in a warm environment for ~30 minutes, or until they have slightly puffed up.
Preheat the oven to 350F / 175C. (Optional, for browning): In a small bowl, whisk together an egg and 1 tbsp. of milk. Brush the tops of each of the buns with the egg wash and a sprinkle of granulated sugar.
Bake the buns for 15-20 minutes, or until they start to turn golden brown. You can also check if they are done by making sure the internal temperature is at least 190°F / 87°C.