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Bring a large pot of generously salted water to boil for the pasta.
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Place the garlic and olive oil into a large pan over medium low heat. Cook, stirring, until the garlic is fragrant and golden, but not browned, 3-4 minutes. Add the mushrooms and thyme or rosemary and raise the heat to medium high. Do not turn or stir the mushrooms for 2 minutes, or until they are browned on the undersides. Toss and let cook another 2 minutes and then toss again.
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Continue cooking the mushrooms for a total of 15 minutes, tossing every 2 minutes, until the mushrooms are cooked all over. Add the zucchini and cook briefly, until crisp tender. You may remove the garlic now (I left it in--we love garlic, and we just ate around it). Stir the ragù into the dish and season to taste with salt and pepper. Mix in the parsley if using. Turn off the heat and cover.
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Add the pasta to the boiling water and cook according to directions for al dente. When you drain the pasta, be sure to reserve 1 cup of the pasta cooking water.
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Toss the pasta with the prepared mushroom sauce. Add pasta cooking water as needed to loosen the sauce. Serve immediately, sprinkled with an Italian hard grating cheese.