Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Drain and reserve ½ cup of the pasta water.
Heat olive oil and butter in a large skillet over medium-high heat. Add the mushrooms and let them cook undisturbed for 4–5 minutes until they start to brown. Stir and cook for another 3–4 minutes until golden and tender.
Add the minced garlic, salt, pepper, and optional red pepper flakes. Cook for 1 minute until fragrant.
Pour in the white wine to deglaze the pan (if using), scraping up any bits from the bottom. Let it simmer for 1–2 minutes until mostly evaporated. Lower the heat and add the cream, stirring gently. Simmer for 3–4 minutes until the sauce slightly thickens.
Add the drained pasta to the skillet and toss to coat in the sauce. If needed, add a splash of the reserved pasta water to loosen the sauce. Stir in Parmesan cheese and adjust seasoning.
Remove from heat and sprinkle with fresh parsley. Serve immediately with extra Parmesan on the side.