Ingredients

1/2 cup warm milk (110-115F)
2-1/2 tsp (9g) active dry yeast
2 tsp honey

5 large egg
1 large egg yolk (1 white removed for milk with dry yeast - original recipe 6 large egg with fresh yeast)
2 tsp vanilla
5 tbsp (2.1 oz) granulated sugar
4 cup + 2 tbsp (17.6 oz) all purpose flour / bread flour
1-1/2 tsp fine salt

1 cup + 2 tbsp (8.8 oz) butter, softened @73-75F, divide into 4 portions (soft = leave mark when poked but NOT melted)

Instructions

Room temp 86F max - otherwise oil will seep out of dough
Higher range temp & humidity - butter will become too soft, dough more liquidy to handle

Day 1 - all done in stand mixer bowl
1. Milk + yeast + honey: whisk & bloom 10-15 min until frothy & bubbly.
2. + egg + yolk: hand whisk to break yolks.
3. + vanilla + sugar + flour + salt (salt over flour, do not touch yeast): by hand with dough hook, mix to scraggly dough.
4. Dough hook - knead Sp2 1 min.
5. + 1 portion butter (1 tbsp at a time): knead Sp2 3 min. Scrap.
6. Repeat with remaining 3 portions of butter. (total butter knead time 12 min).
7. Knead Sp6 5-15 min (do not go by time, go by dough condition) - until droopy water balloon dough able to be lifted up by dough hook for 1-2 sec, albeit droopy and wet, with more-or-less clean bowl; & touch is very soft, wet, tacky but do not stick to finger too much; & visual is smooth, shiny, satiny; & pull a sample out for window pane test (stretches but do not break).
8. Flour table, turn dough out.
9. Flour hands, fold dough edge to middle to form smooth ball. Flip over tighten up bottom w/ heel of hand to a tight ball.
10. Place dough ball in large bowl. Cover & proof (72F) 1-2.5 hour, until double/triple.
11. Flour table, turn dough out.
12. Flour hands, deflate, reshape to proofing ball again, go back in bowl.
13. Cover, chill in fridge 24 hours.

Day 2
1. Butter & dust 2 pans - 8.5x4 or 9x5.
2. Flour table, turn dough out, deflated, divide into 2 by weight.
3. Nantaise brioche loaf - divide in 8 by weight, fold to form smooth top ball, cup top & roll on table to seal bottom seams, place dough in pan in zig-zag pattern, cover.
4. Braided brioche loaf - divide in 3 by weight, roll out to 14" rope, pich ends together to seal, braide without stretching dough, tuck pinches ends under, place in pan, cover.
5. Proof 2 hours until double (do not go by time, go by dough condition) - when poked,
bounce back completely = under-proof
bounce back slightly / halfway = ready to bake
does not bounce back = starting to be over-proof, bake right now
deflate = over-proof, do not bake, will collapse - deflate, reshape & re-proof again
6. Preheat 325F.
7. Egg wash.
8. Bake 30-45 min - until golden brown & internal temp 180F-190F.
9. Remove from oven. Let cool 5 min.
10. Flip onto wire rack to cool completely.