To make the court-bouillon, put all the ingredients in a large pan with 3 litres of water. Bring to a simmer and bubble gently for 20 minutes. Strain through a fine sieve.
Pour the court-bouillon into a fish kettle. Add the sea bass, placing it on the trivet. Bring to a simmer, put on the lid, then turn off the heat and leave for about 40 minutes, until the fish is cooked through.
Remove the fish and transfer to a platter. Don’t skin it yet.
To make the mayonnaise, put the egg yolks, salt, sugar, pepper, mustard and lemon juice in a blender and process until smooth (or whisk by hand). Combine the two oils in a jug.
With the processor running (or whisking by hand), start pouring in the oil in a trickle. When the mixture starts to emulsify, you can pour a little faster. When all the oil is added, you should have a thick mayonnaise.
Combine the anchovies, garlic, capers and parsley on a board and chop them all together as finely as you can. Stir them into the mayonnaise. Taste and adjust the seasoning. Chill until ready to serve.
To serve, peel the skin from the upper side of the fish. Bring the whole fish to the table. Gently ease portions of the fish away from the backbone and place on plates.
When you’ve done the first side, lift off the backbone, head and tail and gently break the remaining side into portions. Accompany with the salsa verde mayonnaise, plus some dressed puy lentils and perhaps new potatoes and a leaf salad.