1: Seven days before you plan to cook, make the brine. Mix all the brine ingredients together in a saucepan and bring to the boil, stirring to dissolve the salt, sugar and saltpetre. Boil for 5 minutes, then remove the pan from the heat and leave the brine to cool to room temperature.
2: Pierce the beef brisket all over with a skewer and then place it in a non-metallic container. Pour over the brine, making sure that the beef is completely covered. It may need weighing down. Cover the container and put in the fridge for 7 days.
3: After 7 days, remove the beef from the brine and rinse it in running cold water. Place the beef in a large saucepan and add all the ingredients for the braising vegetables. Pour in enough cold water to cover the ingredients and bring to the boil, skimming the surface, as necessary. Turn the heat down to low and leave to simmer, uncovered, for 2½ – 3 hours until the beef is tender. Remove the pan from the heat, and leave the beef to cool completely in the stock, uncovered, which will take a couple of hours.
4: When cool, remove the salt beef from the liquid and pat dry. Cover and chill until needed, when it can be sliced and served hot or cold. Keep some of the cooking liquid to reheat the beef in if you’re planning to serve it hot.
5: First, make the pickled vegetables. Combine the mushrooms, carrots, cucumbers, radishes and shallots in a large non-metallic bowl. Stir in the pickling mix, cover with clingfilm and leave for 2 hours at room temperature.
6: Meanwhile, make the black pepper cream cheese. Beat the cream cheese until it is soft, then add the cracked black pepper and a pinch of salt. Cover and chill until needed. When you’re ready to assemble the sandwiches, preheat the grill to high and bring the water or beef braising liquid to the boil. Place the bagels under the grill and toast both halves, then spread with the cream cheese.
7: Add the butter to the boiling liquid and stir until it melts. Drop the salt beef into the liquid and leave for 1–2 minutes to warm through. When the beef is warm, divide the slices between the bagel bottoms, sprinkle with fresh dill and top with the bagel tops.
8: Serve with the pickled vegetables and enjoy!