Mix the yeast, lukewarm milk and sugar and let it sit for 5 minutes until it foams up.
In the bowl of a stand mixer fitted with dough hook attachment, add flour, salt and eggs. Once the yeast mixture is foamy add to the flour mixture. Mix to combine well. The dough will start out shaggy, but quickly comes together once you start adding in the butter.
Add the butter, a few pieces at a time, and 'knead' in the mixer for another 15 minutes at Level 2 speed. The dough becomes quite sticky as the butter is mixed in and should easily come free from the bowl.
Place the dough in a greased bowl, cover with a damp linen towel and let it rise at room temperature for one hour or double in size. Refrigerate for 4 to 16 hours. This is what makes the Brioche super soft.
Take the dough from the fridge, place on a lightly floured surface and form into a loaf. Place it into a bread pan or brioche pan and let rise another 1 1/2 to 2 hours or until double in size.
Preheat oven to 400 degrees. Once up to temp, reduce heat to 375 and bake the bread for 30 to 35 minutes until the top is nicely browned. Allow to cool on a rack before slicing.