Combine the brine ingredients in a saucepan with enough cold water to cover the beef. Bring to a gentle simmer, stirring to dissolve the salt and sugar. Allow to cool completely and transfer to a clean bowl with the beef. Ensure the beef is completely submerged (I weighed mine down with a Kilner jar filled with rice). Place this in the fridge for five days.
When the time's up rinse the beef and place in a saucepan with the chopped veg. Cover with water, bring to the boil then gently simmer for 3 - 4 hours until you can poke a knife into the meat with no resistance.
You can serve the beef straight from the broth, else allow to cool. Carve thickly and reheat in a shallow frying pan with the butter and stock for a couple of minutes. Serve with a toasted bagel and your choice of mustards, sauerkraut, gherkin, mayo, cream cheese or whatever condiments do it for you.