In the bowl of a stand mixer, dissolve the yeast in the water. Add the flour, sugar, egg, salt and 3/4 of the milk.
Start kneading on low speed (speed 1 on a KitchenAid). Gradually add the remaining milk to form a soft dough that is not sticky. Knead for about 12 minutes.
Add the butter gradually, a little at a time, while continuing to knead. Scrape down the sides of the bowl if needed.
Continue kneading for another 12 minutes on speed 2, until you get a smooth, supple and well combined dough that wraps around the hook. If you stretch a small piece of dough to form a thin sheet, it should not tear.
If this is not perfectly achieved, it is not a problem, as we are not aiming for a very stretchy crumb like a bakery style brioche. You can try a different flour next time.