Place the milk in a small saucepan over a medium heat until it begins to steam. Remove from the heat and leave to cool until it's warm to the touch but not hot.
Put the flour in the bowl of a free-standing mixer fitted with a dough hook. Place the salt and sugar on one side of the bowl and the yeast on the other side. Add the warm milk and 5 eggs and mix on a slow speed for 2 minutes, or until all the flour has been incorporated, then mix on a medium speed for 8 minutes. Gradually add the cubed butter, piece by piece, and mix for a further 5 minutes, scraping down the sides of the bowl to ensure the butter is thoroughly mixed in. The dough should feel soft but not too sticky.
Grease and line a 24 x 14 x 7cm loaf tin with greaseproof paper. Tip the dough into a large lightly greased bowl and cover with clingfilm. Leave to rise for 1-2 hours somewhere warm but not too hot as the butter in the dough will begin to melt and make it too soft. Once risen, place in the fridge for 1 hour.
Preheat the oven to 180°C/fan 160°C/gas mark 4. Remove the cooled dough from the fridge and knead lightly for 2-3 minutes to knock back the air. Divide into 7 even pieces. Working with one piece at a time and keeping the remaining dough covered, shape each piece into a smooth ball by repeatedly tucking the dough under itself. Bring the top of the roll down and tuck it underneath itself to make the surface taut. Keep them covered with clingfilm while you repeat this process with the remaining dough.
Place the balls in the loaf tin at a slight angle to each other so the pattern is slightly uneven. Cover with clingfilm and leave to prove in a warm area for 30-45 minutes, until it has doubled in size again. Beat the remaining egg and brush the top of the brioche with the egg wash. Bake for 35-40 minutes, until risen and deep golden all over. Leave to cool in the tin for 10 minutes before transferring to a wire rack to cool.