Preheat the oven to 300°F (150°C/Gas mark 2).
Put two of the heads of garlic and all the shallots between two layers of kosher salt in an ovenproof dish and cook in the oven for 1 hour 30 minutes. When they are cooked, cut the shallots in half lengthways and squeeze the soft garlic from the heads. Set aside.
Reduce the oven temperature to 250°F (130°C/Gas mark ½).
Clean and scale the four sea bream. Remove the two fillets from each fish by slicing lengthways along the backbone on either side, but leaving the fillets attached at the belly. Clean the fish, remove the bones and skin, and lay them side by side in an ovenproof dish. Season, pour over 1 cup (250ml) of the stock, and cook in the oven for 15 minutes.
Remove any bones or pieces of skin from the white fish fillets, put the remaining stock in a saucepan, and add the fillets. Separate the third head of garlic into cloves, peel them, and add to the saucepan. Cook for 30 minutes. Remove the saucepan from the heat, add the cream and two sage leaves, and allow to infuse for a few minutes. Remove and discard the sage leaves. Pour this bouillon into a liquidiser and blend until smooth. Add salt and pepper to taste.
Pour a little bouillon into each soup plate and lay a sea bream fillet in the centre. Arrange three shallot halves and a sage leaf around it, then place a quenelle-shaped teaspoonful of the reserved garlic puree on top.