Peel the shrimp when they’re still partially frozen, reserving the shells. Once peeled, cover and refrigerate the shrimp until you’re ready to cook.
Cover the morels in warm water and soak for 30 minutes. Once rehydrated, squeeze the morels to extract moisture. Transfer to a cutting board and slice the larger ones into quarters.
Dry the thawed cod with a tea towel or absorbent paper— frozen cod tends to express moisture as it thaws, and you want it to be quite dry before sautéing.
Heat 1 tablespoon of oil and 1 tablespoon of butter in a 10-inch frying pan over medium heat.
When butter is melted and sizzling, add the shrimp to the pan, in batches so as not to crowd them. Cook about 1½ minutes per side, until pink and no longer translucent, removing each batch to a plate as it’s done. Don’t worry if shrimp are slightly undercooked. To the same pan, add another tablespoon of oil. Add mushrooms and garlic, and cook for about 5 minutes. If mushrooms stick to the pan, add a splash of white wine. Remove the mushrooms to another plate.
Add 1 tablespoon of oil and 1 tablespoon of butter to the pan. Once butter is sizzling, add the pieces of cod and sauté for 1 minute per side. (Cod is easy to overcook.) Remove to a plate and reserve.
Add tarragon, white wine, and shrimp shell stock to the pan, turn heat to medium high and cook until reduced by ½. Add cream and reduce until thick enough to coat the back of a wooden spoon. Reduce heat to medium low.
Add shrimp, morels, and cod to pan for 1–2 minutes to warm up. Spoon into 4 soup plates and serve at once.
Optional: serve with linguine tossed with oil, garlic, and parsley. Start the linguine cooking while you’re reducing the white wine and shrimp sauce.
