In a bowl, mix together milk and vinegar and set aside for 10 minutes. It will curdle. Your buttermilk is ready.
In a larger bowl, mix together flour, salt, sugar and instant yeast.
Make a well in the center and add buttermilk.
With a spoon, roughly mix the flour to incorporate the liquid. At this stage, the dough may seem a bit dry — but after you add the butter, the consistency will change.
Now add the butter and mix until it is incorporated into the dough. The dough will become very sticky.
Dust two tablespoons of flour on the counter and transfer dough to the counter.
Start kneading. Do not be tempted to add more flour. Keep on kneading for 15 minutes. Use a dough scraper to make kneading easier.
After kneading, the dough will become soft and elastic, and lose its stickiness. To test whether you've kneaded enough, take a small piece of dough and stretch until there is a thin film in the center. It should be sturdy enough not to break, but when you place it before light, it should be translucent. This is the windowpane test: If the dough passes, it is ready for its first proof.
Oil a clean bowl, place the dough in it and coat the top of the dough with oil. Cover with cling wrap and set aside until it doubles in volume. The time this will take depends upon the temperature of your kitchen — it will take less time if it's hot, and longer if it's cooler. If it is very cool in your kitchen, place the dough inside a warm oven with oven switched off. Do not over-proof the dough; keep checking it.
Once your dough has doubled in size, transfer dough to counter and press it to release the gas bubbles. Shape it into a 7" * 12" rectangle. Roll it tightly into a log, keeping the 7" width intact.
Place the roll seam side down in a buttered loaf tin. Cover with cling and set aside until it doubles again.
After 15 minutes, preheat oven to 400 degrees Fahrenheit. Meanwhile, mix the honey and milk.
Apply a coat of this milk to the doubled dough. Place it in preheated oven and bake for 20 minutes in the middle rack. The top will start browning fast. After 20 minutes, move the loaf to the lowest rack, cover with aluminum foil and bake for another 30 minutes.
Remove the brioche from the oven, and allow it to cool on a wire rack for 10 minutes. Then, with the help of a spatula, loose the sides of the loaf in the tin and remove the loaf.
Let it cool completely on the wire rack. When it's cool, slice it evenly with a bread knife and enjoy!