Boil the pasta. Bring a large pot of salted water to a boil. Cook the pasta until just shy of al dente. Reserve 1 cup of pasta water, then drain.
Sauté the mushrooms. In a large skillet, heat olive oil and butter over medium-high heat.
Add mushrooms in an even layer. Let them brown undisturbed for 3–4 minutes, then stir and cook until golden and tender. Season with a pinch of salt and pepper.
Add aromatics. Reduce heat to medium.
Add the chopped onion and cook until soft and translucent, about 3 minutes. Stir in the garlic, thyme, and red pepper flakes, and cook for 30–60 seconds until fragrant.
Deglaze with white wine. Pour in the wine and scrape up any browned bits from the pan. Simmer for 2–3 minutes, until the alcohol cooks off and the liquid reduces by about half.
Pour in the cream. Lower the heat and add the cream.
Simmer gently for 2–3 minutes, stirring, until slightly thickened. If it looks too thick, add a splash of pasta water.
Wilt the spinach. Add the spinach and stir until it softens and blends into the sauce, about 1 minute.
Toss with pasta and Parmesan. Add the drained pasta to the skillet. Sprinkle in the Parmesan and toss until the sauce clings to the noodles.
Add pasta water as needed to loosen and create a glossy, silky coating.
Finish and season. Taste and adjust salt and pepper. Add a little lemon zest or a small squeeze of lemon juice to brighten the flavors.
Serve. Plate with extra Parmesan and a crack of black pepper. A drizzle of good olive oil on top is a nice touch.