In a large bowl mix flour, dry yeast, sugar & salt.
Add milk, eggs & butter.
Mix w/ the dough hooks of the handheld electric mixer until it's well done.
Form a ball of the dough, cover the bowl w/ a tea towel (or whatever) & put it in the oven; heat the oven for about 2-3 min at about 75° C w/ fan.
Let the dough rise for about 1 h.
Distribute some flour on a board ... Transfer the dough from the bowl onto the board. Knead the dough, form a loaf & cut it into 4 parts. Knead each part, flat it w/ your hands & fold it several times (6-8 times).
Line a tin loaf w/ baking parchment & arrange the dough.
Put the loaf tin in the oven; heat the oven for about 2-3 min at about 75° C w/ fan.
Let the dough rise for about 30 min.
Preheat the oven to 160° C w/ fan.
For the topping: whisk the egg & brush it all over the dough; add the coarse sugar.
Put the loaf tin in the preheated oven & let it bake for about 25 min. Make the famous test w/ a thin wooden pin ... If necessary add another 5min.
Let the brioche bread cool down & start enjoying.