Start with the brisket. Heat the oil in a large oven-proof pan, over a high heat. Pat the salt and pepper all over the brisket. Place the brisket in the pan and seal on all sides (should take about 6-8 minutes).
Turn down the heat and add in the tomato puree, thyme, brown sugar, stock and the garlic. Stir and bring to the boil. Turn off the heat, place a lid on the pan and place in the oven to cook for 3 hours, until tender. Check once or twice in the last hour of cooking an top up with a little hot water from the kettle if needed.
Make the coleslaw by mixing all of the coleslaw ingredients together. Cover and refrigerate until it's time to serve.
Place the potatoes in a pan of cold water. Bring to the boil and simmer for 5 minutes. Turn off the heat and drain off the water. Carefully give the pan a shake to 'fluff-up' the potatoes slightly.
When the beef is about 15 minutes away from being finished, make the sauté potatoes. Heat the oil on a high heat in a medium frying pan. Place the potatoes in the pan and cook on high, turning often until golden brown. Turn off the heat, allow to cool for 30 seconds, then add the garlic to the pan (adding the garlic earlier will cause it to burn, giving it a nasty acidic taste). Give it a stir, to infuse the garlic flavour in the potatoes, then remove the potatoes from the oven with a slotted spoon. Place on kitchen paper to remove excess oil. Sprinkle on the salt and pepper.
Remove the beef from the oven. Place the beef on a chopping board (don't throw away the stock - it makes delicious gravy), and shred using two forks.
Make up four mounds of shredded meat and place them on a grill/baking tray. Top the meat with the grated gruyere.
Brush the insides on the brioche rolls with the olive oil. Place on the grill tray with the meat. Grill until the cheese is melted and the buns are lightly toasted on the inside.
Now it's time to assemble.
Place the bottoms of the buns on plates. Top with lettuce leaves and divide the potatoes between the four buns. Top each with once of the mounds of brisket and spoon a heaped tablespoon of coleslaw onto each. Place the tops on the buns and serve immediately!