1. In a skillet bring the vermouth, shallot and parsley to a boil. Lower the heat and simmer ten minutes. Add the sole and poach gently until the fish flakes easily when tested with a fork. There should be enough of the wine to cover the fish. Add more wine if necessary.
2. Remove the fish to a flat baking dish, season with salt and pepper and keep warm. Boil the liquid until it is reduced to one-half cup.
3. In the top of a double boiler, mix the cooking liquid, butter and egg yolks. Whisk the sauce with a wire whisk over simmering water until it thickens. Add the heavy cream and pour the sauce over the fish fillets. Set under a hot broiler for a few seconds to glaze the top and serve at once.