Mix the yeast, lukewarm milk, and sugar, and let it sit for 5 minutes until foaming. Mix in the eggs until well combined.
Place it with the flour and salt in the bowl of a stand mixer, and knead at speed level 1 for 5 minutes (your dough is very sticky). Add the butter in pieces and knead for another 15 minutes at speed level 2 (your dough should be sticky but comes easily from the bowl using a silicone spatula).
Place the dough in a greased bowl, cover with a damp tea towel, and let it rise at room temperature for one hour. Refrigerate for 4-16 hours ➝ makes your brioche soft & airy.
Take the dough out of the fridge, place on a lightly floured surface, divide into five pieces and fold each one into a log (punch down the dough gently with the ball of your hand, stretch into a rectangle, and roll up into a log). Place them in a greased (or with parchment paper lined) 10x5-inch loaf pan (25x12cm), cover with a damp tea towel and let it rise for 1.5-2 hours at room temperature.
Preheat the oven to 395°F/200°C. Brush the dough with the egg wash and bake it for 30-35 minutes until brown.
Allow the brioche to cool down on a cooling rack before slicing.