Mix the dough with stand, mixer, bread machine dough setting or by hand.
Put the flour the mixing bowl add the yeast, salt, sugar on different edges of the bowl and the butter in the middle. Put the milk and water in a jug. Add the milk and water to the bowl and start the mixer on a slow speed. When all the ingredients are combined, switch to a medium speed and mix for 6 minutes. Cover the bowl and leave to rise.
Make a square of the garlic butter for laminating 17cm x 17cm: This is done as follows. Take 2 pieces of greaseproof paper and on piece arrange slices of the butter in a square about 15 or 16 cm. Cover with the 2nd piece of greaseproof paper and using a rolling pin even out the butter, expanding it slightly to make the 17cm square. In squaring it up, trim to make straight edges, putting the excess pieces to fill any obvious gaps or put back on top to be rolled out evenly.
Put the butter back in the fridge to harden and wait until the dough has risen.
When the dough has risen, roll out carefully to make a square 26cm x 26cm
Put the square of butter diagonally on the dough square and fold the edges of the dough to make a sealed square envelope and seal the seams by pressing lightly with your fingers.
Roll the dough, starting from the centre and working outwards each direction, to create an oblong 20cm x 60cm
Fold 1/3 of the length into the middle and from the other end fold 1/3 of the length back into the middle, like folding a letter. You should now have square of dough 20cm x 20cm
Cover with cling film and put in the fridge for an hour. To make the handling easier, I cut a square of stiff cardboard just over 20 x 20. I put the cling film wrapped dough on the card and put the whole thing in a sealable plastic bag.
After an hour, take the dough from the fridge, turn 90 degrees and roll again 20cm x 60cm. Fold like a letter back to 20cm x 20 cm. Rewrap with cling film and put back into the fridge.
After 1 hour, repeat this last step again. You will now have 27 layers of laminated dough.
Leave in the fridge overnight.
Take the dough from the fridge. The next steps needs a long clear work surface. Roll the dough to make a long oblong, 21cm x 100cm
Using the tapemeasure and the pizza wheel, cut the dough lengthways in to 3cm strip.
Along the length, mark off every 25cm and cut into 25 cm pieces.
Roll each piece starting from the narrower 21cm edge. Using baking scraper cut into pieces about 3cm and stand in cupcake baking tray
Beat the egg with 2tsp of water. Using a brush coat the dough with the egg. Cover and leave to rise. This can take 1 1/2 to 2 hours. In the meantime heat the oven to 195ºC.
When the dough has risen, gently coat with egg once more and place the tray in the oven. Bake for 6 minutes. Turn the temperature down to 165ºC and then bake for a further 12 minutes. Depending on how quickly your oven adjusts temperature settings, opening the door for a few seconds and closing it can help reduce the temperature and this is quite safe during the baking.
The garlic brioche should be a golden colour. Take out of the oven and place on a cooling rack.
Best eaten warm.