Heat all the brine ingredients in a pan with 2.75 litres of water until it comes to a boil. Turn it off and allow to cool. Place the brisket and brine in a tub, making sure it is completely submerged. You may need to weigh it down. Leave this in the fridge for 7-10 days.
After this time rinse the beef briefly and pat it dry. Put into a pot with the vegetables and simmer for about 6-8 hours, until a knife sinks into it like its butter. Remove from the pot and eat some while still warm. Save half for the corned beef.
To make the corned beef, chop half of the brisket finely and melt some butter. You will need just enough to bind it together. Line a loaf tin with cling film and pack it in. Fold the film over the top and allow to set overnight in the fridge. Slice thickly and pile into sandwiches