Preheat oven to 250C. Prepare 2 large bowls filled with iced water.
For the Mud crab, bring 4 litres of water to salted water to the boil. Remove legs from mud crabs and reserve for the Sauce.
Place remaining crab and claws, into water, cover and cook for 12 minutes. Refresh in a bowl of iced water then drain well. Crack shell open, remove flesh from body and shred finely. Set the shredded crab meat aside in a medium bowl in the fridge until needed for plating. Crack claws open and carefully remove flesh in whole pieces and reserve, in the fridge, for plating.
For the Sauce, use a cleaver to slightly crush the reserved crab legs. Place crushed crab legs into a small, flame-proof roasting pan along with the bacon and roast in the pre-heated oven until caramelised, about 20 minutes.
Transfer pan onto the stove top over medium high heat. Deglaze the pan with the green apple juice then add vinegar and lemon juice. Reduce heat and simmer until reduced by ¼.
Strain the stock and transfer to a small saucepan over low heat. Whisk in 100g of the butter and simmer to reduce slightly. Whisk in the remaining butter and the cream until incorporated. Simmer on low heat until reduced by half. Strain through a fine sieve and place into a serving jug, keeping warm, until needed.
For the Apple, use a mandolin to slice the apple into 2 mm slices then cut each slice into 2mm wide matchsticks. Place the matchsticks into a small bowl and toss with juice of ½ lemon. Cover the bowl with cling film and set aside in fridge until needed.
For the Cauliflower Purée, place the cauliflower into a food processor and process to a crumb. Transfer to a medium saucepan and the milk, cream, butter and salt and pepper to taste. Simmer over medium heat until cauliflower is tender, about 15 minutes.
Once cauliflower is cooked, remove from heat and strain, reserving all cooking liquid. Place the cauliflower in a stick blender canister along with half the cooking liquid. Use a stick blender to puree the cauliflower until smooth, adding more cooking liquid if needed to reach desired consistency. Pass the purée through a fine sieve, adjust seasoning if necessary and set aside, keeping warm, until needed.
For the Cauliflower Pickle, place the water, vinegar, sugar and salt and pepper to taste in a medium saucepan and bring to the boil.
Meanwhile, cut cauliflower into florets, then slice each floret into 3mm thick slices. Once pickling liquid is boiling, remove from heat. Add the cauliflower slices and set aside in the pickling liquid for 10 minutes. Drain and set Pickled Cauliflower aside until needed.
For the Crispy Brussel Sprouts, first peel and reserve 16 of the larger, outer leaves of the sprouts for the Blanched Brussel Sprouts.
Cut each sprout in half and shred finely. Place a medium fry pan over medium high heat and add 20g butter and 20ml oil and when hot, add shredded sprouts and sauté until soft, about 5 minutes. Remove the sprouts from the pan and place on layers of kitchen paper to drain off the butter and oil.
Once drained, return the shredded sprout leaves to the pan over medium heat. Fry, tossing gently, until golden and crisp. Remove from pan, season to taste and set aside, keeping warm, until needed.
For the Blanched Brussel Sprouts, place the salt in a small saucepan of water, place on the stove top over high heat and bring to the boil. Place the reserved outer brussel sprout leaves in the boiling water and blanch until bright green, about 30 seconds. Remove immediately from the boiling water and plunge into the bowl of iced water to refresh. Drain the leaves and set aside until needed.
To serve, place 3 spoonsful of Cauliflower Purée in a crescent shape on the serving plates and smooth gently with the back of the spoon to level. Place 4 Blanched Brussel Sprout leaves along puree, at intervals, facing upwards to make a cup. Sprinkle a little of the Crispy Brussel Sprouts in and around the purée. Fill the Blanched Brussel Sprout leaves with shredded Mud crab flesh. Arrange 3 pieces of Pickled Cauliflower next to the leaf cups and top with claw meat. Spoon warm Sauce in and around claw meat. Remove Apple matchsticks from fridge, drain and pat dry. Scatter matchsticks around the Blanched Brussel Sprout cups, along the crescent shaped line of the purée. Serve remaining Sauce on the side.