Rinse the fish (inside and out) in cold water, pat dry, season with salt (inside and out). Place the carrots and fish on a baking tray lined with baking paper. Spread the butter over the top.
Bake for approx. 30 mins. in the centre of an oven preheated to 200°C.
Beat the egg yolk, mustard, lemon juice and saffron in a bowl using the whisk on a hand mixer, add the oil drop by drop to begin with, then more gradually, stirring constantly. Add the vinegar and parsley. Serve the saffron mayonnaise with the fish.