Cook pasta in a large pot of boiling, salted water until barely al dente.
While the pasta is cooking, heat 2 tablespoons butter and oil in skillet over moderately high heat until foam subsides, then sauté mushrooms, stirring until golden, about 4 minutes. Add zest and garlic and sauté, stirring, until mushrooms exude liquid, about 3 minutes. Add Worcestershire sauce and lemon juice and cook until most of liquid is evaporated, about 2 minutes. Stir in thyme, pepper and remaining ¾ teaspoon salt.
Reserve 1 cup pasta cooking water, then drain pasta in a colander.
Transfer mushrooms to pasta pot, then add ½ cup reserved cooking water and bring to a boil. Stir in parsley and remaining 2 tablespoons butter. Return pasta to pot and add cheese, tossing to combine. If pasta seems dry, moisten with more cooking water.