Add the buttermilk into a microwave safe bowl. Heat for 30 seconds or until it is lukewarm. IMPORTANT: Do not heat it too much, as it will turn into cream if you do.
In the bowl of your stand mixer, add all your dry ingredients in this order: Instant yeast, all purpose flour, sea salt and sugar. Whisk together to sift for about 30 seconds.
Make a well, add the eggs and the softened butter Mix with a dough hook for about 3 minutes on the lowest setting of your stand mixer. Once the ingredients are almost combined, add the lukewarm buttermilk. Then, increase the speed to the second lowest setting and knead for 10 minutes. Your dough is ready once it holds together and no longer sticks to the sides of the bowl. NOTE: The dough tends to be stickier than with a regular brioche.
RISE & ASSEMBLY
Place the dough rolled into a ball in a clean bowl, cover with a plastic wrap and let it rise for about 2 1/2 hours at room temperature or 2 hours in a turned off preheated oven (100F/37C). It will double in size.
Once the dough has doubled, scrape it out onto the Roul'Pat™.
Knead lightly into a ball. Weight your dough and divide it into 10 segments (Mine was 42.32oz / 1.2kg so 4.23oz / 120g each). Take each segment and roll it into a ball.
Arrange each one into your Round Mold. Starting with 3 at the center and the rest all around. Let it rise for another 1 hour at room temperature or 45 minutes in a turned off preheated oven (100F/37C).
BAKE!
Preheat oven to 350F/180C.
Brush the milk/sugar mixture on top and sides of the brioche.
Bake for 30 minutes at 350F/180C. (Every oven heats differently, monitor your Brioche from 25min). It is ready when golden brown and does not feel hallow to the touch.
Once your Buttermilk French Brioche is out of the oven, let it cool down directly in the mold 10 minutes before demolding onto your cooling rack. Enjoy & Bon Appétit!