Lobster stock should be made from shells and heads, then heavily reduced to make 3-4 tablespoons.
To make the lobster sauce, heat the olive oil in a medium sauté pan and cook the shells and vegetables together for 20 minutes. Add the vermouth and reduce the volume of the liquid by half, then add the tomato purée, chopped tomatoes, star anise and coriander seeds. Simmer for 10 minutes, add enough water to just cover the shells and vegetables and then simmer for 1 hour.
Crush shells and vegetables, then strain the broth into a bowl, discarding the shells and vegetables. Pour the broth back into the pan and reduce until you have a thick sauce. Season with salt and pepper.
Scale, gut and wipe the fish. Rub the inside cavity with salt. If you have a fish kettle, steam the salmon whole over boiling water for 30-35 minutes (making sure the water is kept topped up).
Or wrap the fish in lightly oiled foil and bake it in the oven for an hour at 325 F (170 C) gasmark 3. Leave it to rest while you make the butter.
Warm the lemon juice in a small basin over a saucepan of simmering water.
Beat in the nuggets of cold butter, adding more as each one melts.
Do this gently – it can split if you overheat it (revive it with a quick splash of cold water). When you have an unctuous smooth sauce like thin cream, sieveand whisk in the green goo from the head of the lobster – which immediately turns the butter a wonderful orange-pink.
Serve the salmon when it is just cool but still sweet-flavoured and full of its own juices, with piping hot baked potatoes and warm lobster butter