Step 1Place the mushrooms in a bowl, cover them with hot water and let them soak for 20 minutes. Remove the mushrooms and pour the liquid through a strainer lined with a triple thickness of paper towels to remove any grit, pressing down on the mushrooms. Set the liquid (you should have about 1 cup) aside. Quickly rinse the mushrooms in an unlined sieve to remove any remaining grit and set them aside.
Step 2Heat the oil in a large nonstick skillet over medium-high heat. When hot, add the shallots and garlic and cook, stirring often to keep from scorching, until softened, about 2 minutes. Add the reserved mushrooms and liquid and bring to a boil. Reduce the heat and simmer 5 minutes.
Step 3Add the cream, lemon zest, lemon juice, salt and pepper to taste. Cook until the mixture thickens into a sauce, about 2 minutes. (The recipe can be made to this point a few hours ahead and kept in the refrigerator, tightly covered.)
Step 4Cook the linguine in salted water according to the package directions. Meanwhile, heat the sauce over low heat. When the pasta is cooked, reserve 1 cup of the liquid, then drain the pasta. Stir the pasta into the sauce, turn the heat to high and add the reserved pasta liquid as needed if the pasta is too dry. Taste and adjust the seasoning, including lemon zest and lemon juice. Serve the pasta hot, garnished with lemon wedges; pass the cheese separately.