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 15 minutes, or until the dough passes the windowpane test. (This will happen after the dough has cleaned the sides and bottom of the bowl)
At this point I would recommend covering the bowl with plastic wrap and leaving it to rise overnight in the fridge. If making the buns in one day, cover the bowl with a towel and leave it to rise in a warm environment until doubled in size (~1 hr.)
Once the dough has doubled in size (or after taking it out of the fridge after rising overnight), lightly punch it down to remove excess air.
Portion the brioche into 6 equally sized pieces (50g each), and roll them tightly into a ball. Place them spaced out on a baking tray lined with parchment paper.