See Tips for using a slow cooker. Heat the oven to 150C fan/gas mark 3.5 if not using the slow cooker. For both methods, heat the oil in a large hob-safe casserole (with a tight lid) or large frying pan (if using the slow cooker). Season the beef with salt, then fry in 2 batches over a medium-high heat for approx 5 minutes, turning with tongs, until a deep brown. Return all the beef to the casserole or frying pan, stir in the lardons, shallots, garlic and mushrooms, then cook for 2 minutes. Add the plain flour and cook for 1 minute. Stir in the tomato purée, then slowly add the beef stock and wine (see Tips). Add the bouquet garni, season, cover and either cook in the oven for 2 to 2.5 hours or until the meat is very tender, or transfer to a slow cooker and cook on low for 6 hours.
Put the potatoes in a large pan of cold salted water. Cover, bring to a simmer, then cook gently for 10 minutes or until tender to the tip of a dinner knife. Drain and leave to steam dry in the pan for 10 minutes. Mash or use a ricer, then beat in the butter, milk, mustard and two thirds of the cheese. Season to taste.
Heat the grill to high. To assemble, remove the bouquet garni, and if cooked in the oven, spoon the mash on top of the bourguignon in the casserole, sprinkle with the rest of the cheese, then grill for 5 minutes until the cheese is golden and melted (or see Make Ahead within Tips). If cooked in the slow cooker, transfer the bourguignon to an oven proof dish or pie dish and follow the instruction above for topping with the mash and then grilling. Serve with buttered greens.