To make the pork head bon bons, heat the oil in a frying pan and add the shallot, fennel and garlic. Sweat for 5–8 minutes until softened. Place the mixture in a bowl and then add the pork, apple, lobster, chives and capers. Mix together with your hands and then divide the mixture into small walnut-sized balls. Roll into smooth balls with your hands. Leave to firm up in the fridge for 30 minutes.
Preheat a deep fat fryer to 190C. (CAUTION: hot oil can be dangerous. Do not leave unattended.) Put the flour, egg and pork crackling granules in three separate bowls. Dip each ball in the flour, egg and pork crackling granules. Add the bon bons to the deep fat fryer and cook until crispy and light golden. Transfer to drain on kitchen paper.
To make the lobster tails, preheat the grill to medium. Season the lobster tails with salt and pepper. Place on greaseproof paper on a baking tray and grill for 5–8 minutes, or until piping hot.
Meanwhile, place the butter, sugar, wine, thyme and garlic in a saucepan and season with salt and pepper. Cook over a medium heat until the butter and sugar have melted. When the lobster is cooked, brush the butter mixture on the lobster tails with a pastry brush to glaze.
To make the Jerusalem artichokes, place the artichokes, vinegar, thyme and garlic in a saucepan and cover with water. Bring to the boil then reduce the heat and simmer until the artichokes are tender. Remove the artichokes with a slotted spoon and transfer to a plate to drain. Heat the butter in a frying pan and add the chives and drained artichokes. Fry for a few minutes until lightly coloured. Season with salt and pepper and keep warm.
To make the pork and lobster sauce, melt the butter in a frying pan and add the lobster shells. Cook until lightly coloured. Add the carrot, celery, garlic, onion, fennel, peppercorns, star anise and ginger and cook for 10 minutes or until the vegetables have softened. Add the Cognac and wine and cook down to a syrup. Add the tomato purée, tarragon and parsley and cook for another 5 minutes. Add the stocks and cook until the sauce is reduced right down and thickened. Strain the sauce through a fine sieve.
Take the sauce off the heat and whisk in the butter until it has melted and the sauce is velvety. Stir in the diced apple and chives.
Meanwhile, to make the mushrooms, heat the butter in a frying pan and add the mushrooms. Fry until wilted and then deglaze with liqueur. Season with salt and pepper and stir in the vinegar.
Serve the bon bons, lobster tails, artichokes and mushrooms on warmed plates with the sauce on the side.