Combine water and reserved fish skin and bones in a saucepan. Add bay leaf, parsley, carrots, onion and peppercorns. Cover and let mixture boil slowly for 45 minutes until the liquid has boiled down to about 1½ cups. Strain.
Melt the butter and sauté the mushrooms until tender and lightly browned. Stir in the flour. Add the strained fish stock, cream and salt. Cook 5 minutes. Add 2 tablespoons of this hot liquid to the beaten egg yolks a little at a time to prevent curdling. Stir into the hot sauce gradually and cook over a low flame until thickened.
NOTES : While particularly good as an accompaniment for Fish Pudding, this sauce is an asset for many other fish and meat entrées.