Clean up the fish by taking off the skin and gills. You could ask the fishmonger to do this for you.
Sprinkle on some sea salt and fire up your grill to smoke on the lowest temperature possible. Preferable around 60°C/140°F.
Place some smoke wood with a light smoke profile, like beach, on the charcoal. Put the fish on the grates and close the lid.
In the meantime, we are going to make the French butter sauce by melting a little bit of butter in a pan over low heat.
To that, we ad the shallots and stir it till it turns soft. Then pour in the white wine and the vinegar and let this reduce to about a tablespoon.
Then we add the rest of the butter and whisk it constantly while adding. Make sure you do this over low heat; otherwise, the butter starts to curdle. Keep whisking till the sauce is creamy.
Put the sauce through a sieve, so you get rid of the shallots but keep the flavour. Bring the sauce to taste with a little sea salt and black pepper.
When the fish reaches a core temperature of 60°C/140°F, you take it off the grill and on a plate. Serve it with the butter sauce.