In a small bowl, combine warm milk and sugar, then sprinkle the yeast over top. Let it sit for about 5-10 minutes until it becomes frothy.

In a large mixing bowl, combine flour and salt. Make a well in the center and add the egg mixture along with the activated yeast. Mix until combined.

Gradually add softened butter in small pieces, kneading by hand or with a stand mixer on low speed until the dough is smooth and elastic (about 8-10 minutes).

Shape the dough into a ball and place it in a greased bowl. Cover it with a damp cloth or plastic wrap, then let it rise in a warm place until it has doubled in size (approximately 1-2 hours).

After the dough has risen, gently punch it down to release the air. Divide it into three equal sections, rolling each piece into a log. Braid the three logs together and tuck the ends underneath.

Place the braided dough in a greased loaf pan. Cover it again and let it rise until doubled, around 30-45 minutes.

About 30 minutes before baking, preheat your oven to 375°F (190°C).

Brush the top of the brioche with an egg wash (beaten egg mixed with water) for a glossy finish, then bake for 30-35 minutes until golden brown. The internal temperature should reach 190°F (88°C).