Skin the fillets of turbot, trim off any dark meat from the underside and discard. Butter a flat ovenproof pan large enough to take the fillets without overlapping, lay them in and add the fish stock. Season, cover with buttered paper or foil and bring to trembling point. Transfer to the oven and gently poach for about 4-5 minutes. When cooked, remove the fillets from the stock, cover and keep warm.
Add the champagne to the stock, set over a high heat and reduce by three-quarters, then add the cream and reduce again until it starts to thicken.