Place the mushrooms, lemon juice, and cream in a saucepan over high heat and bring to a boil. Boil for 5 minutes. Strain the mushrooms from the liquid. Set the liquid aside. Set the mushrooms aside and keep warm.
Place the shallot and vermouth in a clean saucepan over high heat and bring to a boil. Reduce by three-fourths. Add the liquid from cooking the mushrooms and reduce by half. Season with salt. Set aside.
In the meantime, melt 20 grams of butter in a frying pan over medium heat. Season the fish with salt and pepper and cook in the butter.
When the fish is cooked, reheat the sauce and, off the heat, stir in the chilled butter. Arrange the cooked fish on individual, heated serving plates and spoon the sauce over the fish. Scatter the cooked mushrooms over the top of the fish.