For the baked crab, preheat the oven to 200C/400F/Gas 6.
Heat a frying pan until medium hot, add the butter and shallots and fry until softened.
Deglaze the pan with the brandy, then add the stock and cook until reduced slightly.
Add the double cream and return to the boil then reduce the heat and simmer for 2-3 minutes, or until just thickened.
Add the mustard, cayenne and lemon juice and season with salt and freshly ground black pepper.
Stir the picked crab meat into the sauce.
Mix the parmesan and breadcrumbs together in a bowl.
Divide the crab mixture among the 4 crab shells and top with the cheesy breadcrumbs. Place onto a baking tray and bake in the oven for 10-12 minutes, or until golden-brown and bubbling.
For the salad, heat the rice wine vinegar, sugar and salt in a saucepan until just simmering. Pour this mixture over the sliced shallot, mix until well combined and leave to marinate for at least 5 minutes (or up to 24 hours).
Place the lettuce, celery and parsley leaves and apple into a bowl and mix together.
Whisk the English mustard, white wine vinegar and olive oil together in a bowl, then season with salt, freshly ground black pepper and a touch of sugar.
Drain the shallot slices, toss with the salad then dress with the dressing.
To serve, place the baked crab onto serving plates and pile the salad alongside.