Add the eggs, milk, sugar, salt, dry yeast, orange blossom water, orange syrup, and the sourdough discards to your stand mixer bowl and give it a good whisk.

Sift the flour and add it to the wet ingredients. Combine until there are no dry flour particles.

Let the dough rest for 20-30 minutes to allow the flour particles to hydrate.

Start kneading the dough at low speed for about 10 minutes or until the dough gets a bit elastic

Add the butter in 3 or 4 times, making sure it's completely incorporated before you add more.

Knead the dough at medium speed until it's very elastic, shiny, the surface has blisters and it's not sticky. You shouldn't need to add more flour. It should pass the windowpane test

Cover the bowl and let the dough rise at room temperature until it doubles in size

Place the dough in the fridge for a cold fermentation for at least 15 h. You can leave the dough in the fridge for up to 2 days

Remove the dough from the fridge and gently deflate it. Cover it and let it rest for 10 minutes

For the round pan: take 8 pieces of dough of 130 - 140 g (4 - 5 oz) shape them into balls, and place them into your round baking pan.

For the rectangular pan: divide the rest of the dough into 4 equal pieces. Flatten them and roll them into logs as wide as your baking pan.

Cover the two pans and let the dough rise unti it's almost at the border of the pans.

Preheat your oven at 350 F

Before baking, whisk the egg yolk and the milk together and brush the brioche with it.

Bake the brioche until it's golden brown or has an internal temperature of at least 96C

For best results, let the brioche cool down to room temperature before cutting through it.