Put the salmon pieces into a saucepan with the Noilly Prat, white sliced spring onions, lemon rind and the stock. Season with salt and pepper and bring to the boil. Cover and simmer for 10 minutes until the fish is cooked and flakes easily when pressed with a knife.
Lift the fish out of the stock and break into pieces, carefully checking for any bones. Keep hot under foil.
Whisk the egg yolks, tarragon, mustard and butter together in a large bowl. Strain the stock, then gradually whisk it into the egg mixture until smooth. Pour into the saucepan, add the cream and green sliced spring onions, then whisk over a low heat for 4–5 minutes until the mixture is frothy and slightly thickened. Take care not to overheat the soup or the eggs will curdle. Taste and adjust the seasoning if needed.
Divide the salmon between 6 shallow serving bowls, pour the hot frothy sabayon around the salmon and garnish with tarragon, if liked. Serve with melba toast.