Bring the fish towards room temperature
Take the halibut out of the fridge about 20 minutes before cooking so it is not fridge-cold when it goes into the pan.
Steam the mussels
Pull away the mussel beards and rinse the shells well under cold running water. Heat a lidded saucepan over a medium heat, add the drained mussels with a splash of water, cover and steam just until the shells begin to open.
Pick the mussels
Drain the mussels through a colander, keeping the cooking liquor. Once cool enough to handle, remove the mussel meat from the shells and check again for any remaining beards. Cover the meat with the reserved liquor and set aside.
Reduce the stock
Pour the chicken stock into a medium saucepan and simmer until reduced by about half.
Add the cream
Stir in the double cream and continue simmering until the sauce has reduced again and thickened enough to lightly coat a spoon.
Season the sauce
Add lemon juice and salt to taste, then keep the sauce to one side until ready to serve.
Blanch the baby leeks
Bring a pan of lightly salted water to a rolling boil. Trim the tops and bottoms from the baby leeks, rinse them well, then boil for 2 to 3 minutes until soft.
Refresh the leeks
Lift the leeks into iced water to stop them cooking, then drain on kitchen paper. Keep the pan of cooking water for the samphire.
Boil the samphire
Near serving time, briefly boil the samphire in the reserved water until tender, then drain and dry on kitchen paper.
Season the fish
Season the halibut lightly with salt just before cooking.
Pan-fry the halibut
Heat a frying pan until hot, add a splash of rapeseed oil, then carefully lay in the halibut. Cook for 2 to 3 minutes, until the base is beginning to turn opaque, spooning the hot oil over the fish as it cooks.
Turn and finish
Gently turn the fish over to finish cooking. Add the baby leeks to the pan so they colour on one side.
Baste and rest
Add the unsalted butter and a squeeze of lemon juice to the pan. Baste the fish and leeks, then lift them out, spoon over the pan juices and leave the fish to rest briefly.
Warm the mussels
Gently reheat the cream sauce, then add the picked mussels and warm them through without boiling hard.
Plate the dish
Divide the mussels and cream sauce between two bowls. Arrange the samphire and baby leeks in the sauce, then place the rested halibut on top and serve straight away.