Bring a large pot of salted water to a boil. Cook the pasta until just al dente according to the package directions. Reserve 1 cup of pasta water, then drain.
While the pasta cooks, heat the butter and olive oil in a wide skillet over medium-high heat. Add the mushrooms in a single layer, working in batches if needed. Cook without stirring for 3 minutes, then toss and cook until browned and their liquid has evaporated, 5 to 7 minutes.
Add the shallot and cook for 2 minutes. Stir in the garlic and thyme for 30 seconds. Pour in the vegetable broth and scrape up the browned bits.
Lower the heat to medium-low. Stir in the cream and simmer gently for 2 to 3 minutes; do not let it boil hard. Add Parmesan a handful at a time, stirring until smooth. Season with lemon juice, salt, and pepper.
Add the drained pasta and toss to coat. Loosen the sauce with reserved pasta water, a few tablespoons at a time, until glossy. Stir in parsley and serve with extra Parmesan.