To make the artichoke purée, heat the butter in a large pan until foaming. Add the artichokes and salt and cook on a high heat for 10 minutes, stirring constantly.
Reduce the heat to medium and cook for 1 hour. Use a grill scraper or wooden spatula to occasionally scrape the bottom of the pan, as the artichokes start to caramelise.
When the mixture is thick, dry and golden-brown, stir in the cream then blend to a smooth purée in a food processor.
Pass the mixture through a chinois or fine sieve. Place a layer of cling film on the surface to prevent a skin forming, and allow to cool.
To make the artichoke skins, heat the oil in a deep-fat fryer to 150C (CAUTION: hot oil can be dangerous. Do not leave unattended.). Deep-fry the artichokes for 4 minutes. Remove and allow to cool for 2 minutes.
Slice the deep-fried artichokes in half lengthways and peel the skin from the raw flesh. Slice each piece of skin in half to make four pieces per artichoke. Return the skins to the fryer and fry for 3 minutes, or until golden brown and crisp.
Remove the skins from the fryer and leave to dry on a kitchen paper.
To make the charred mussel stock, heat a large saucepan (with a lid) until hot. Add the mussels, wine and 150ml/5fl oz water to the hot pan and replace the lid. Steam the mussels for 2 minutes, then pour the contents through a colander into another pan to catch the stock. Discard any mussels with broken shells and any that refuse to close when tapped.
Heat a dash of oil in a non-stick pan over a high heat. Remove the mussel meat from the shells and fry until they char. Return the mussels and add the mushrooms to the pan of mussel stock and reheat until it starts to simmer. Turn off the heat and set aside for 20 minutes. Pass through a muslin cloth into a clean pan. Discard the mussels and mushrooms.
Put 100ml/3½fl oz of the stock in a new pan and add the rhubarb juice. Bring to a simmer. Slowly emulsify the smoked butter into the stock and dissolve one piece at a time, using a whisk.
To make brown butter, slowly warm the butter until melted. Continue on a low heat, until it changes to a light nutty brown colour. Pour through a fine sieve into a tub ready for serving.
To serve, evenly dress the scallops in the mussel and rhubarb sauce, sprinkle with salt, and leave to marinade for 5 minutes.
Warm the artichoke purée and place a spoonful in the base of a bowl.
Blowtorch the scallops until charred, blackened and cooked.
Dress the charred scallops in the brown butter and sprinkle in a little more sea salt. Top the scallop with the artichoke skin crisps.
Add the samphire and rhubarb dice to the mussel and rhubarb sauce and spoon over at the table.