Make the dough: In the bowl of your stand mixer, add the ingredients in this order: egg, milk, flour, sugar, salt and yeast. (Place the yeast, sugar, and salt in separate places.)Mix with the dough hook for 4 minutes on low speed, then for 6 minutes on medium speed. *The dough is slightly stiff at the end of this step, it's okay.* Set the mixer to low speed again and add the softened butter cubes one at a time. Knead the dough for an additional 6 minutes. (To ensure the dough's consistency, use a bowl scraper to remove any dough stuck to the bowl between mixing cycles.) *The dough will be a little sticky at the end of this step*
Rest: Shape the dough into a ball and place in a greased bowl. Cover with plastic wrap or a clean kitchen towel and freeze for 1 hour at 39°F (4°C).
Grease a 9*13 inch glass baking pan or round baking pan.
Shaping: When the dough is ready. Remove it from the freezer. Divide into 12 equal pieces and shape each into a soft ball. A bench scraper is always useful for dividing and shaping enriched dough. Place them in the prepared baking pan.
Rise: Cover the shaped rolls with plastic wrap or a clean kitchen towel. Allow to rise in a warm environment for 60-90 minutes or until it puffs up. *The ideal temperature for brioche rising is 82°F (28°C).*
Set the oven rack in a lower position and preheat the oven to 320°F (160°C).
Egg wash: Egg wash: right before baking, whisk together the egg yolk and 2 tablespoons milk. Brush egg wash over the tops of the rolls with a pastry brush. Sprinkle pearl sugar over the top of each roll.
Bake: Bake for 30-35 minutes or until golden brown on the top. If it's browning too quickly, cover with aluminum foil or parchment paper after 15 minutes.