Boil the pasta: Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente.
Reserve 1 cup of starchy pasta water, then drain.
Brown the mushrooms: Heat olive oil and butter in a large skillet over medium-high. Add mushrooms in a single layer with a pinch of salt. Cook undisturbed for 3–4 minutes, then stir and cook until browned and reduced, about 6–8 minutes total.
Add aromatics: Lower heat to medium.
Stir in shallot and cook 2 minutes until softened. Add garlic, thyme, and a pinch of red pepper flakes. Cook 30 seconds until fragrant.
Deglaze: Pour in white wine (or broth).
Scrape up browned bits and simmer for 1–2 minutes until slightly reduced.
Create the sauce: Stir in cream. Simmer gently 2–3 minutes to thicken slightly. Season with salt and black pepper.
Add spinach: Fold in spinach and let it wilt into the sauce.
It should shrink quickly.
Toss with pasta: Add cooked pasta and half the Parmesan. Splash in reserved pasta water as needed to loosen and create a glossy, silky sauce that clings to the noodles.
Finish and serve: Taste and adjust seasoning. Add remaining Parmesan and a squeeze of lemon or a little zest for brightness.
Serve hot with extra cheese and cracked pepper.