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.
Prep the mushrooms. Wipe mushrooms clean and slice evenly.
Avoid washing under running water if possible; mushrooms absorb moisture and won’t brown well.
Sauté in batches. Heat 1 tablespoon butter and 1 tablespoon olive oil in a large skillet over medium-high. Add half the mushrooms in an even layer. Cook undisturbed for 3–4 minutes, then stir and cook another 2–3 minutes until golden.
Season with salt and pepper, then transfer to a bowl. Repeat with remaining mushrooms using the rest of the butter and oil.
Build the aromatics. Reduce heat to medium. Add the shallot to the empty pan and cook 2 minutes until softened.
Stir in garlic and thyme; cook 30 seconds until fragrant.
Deglaze with wine. Pour in the white wine and scrape up browned bits. Simmer 2–3 minutes until reduced by about half. If skipping wine, add a splash of broth instead.
Make it creamy. Stir in the cream and nutmeg.
Bring to a gentle simmer for 2–3 minutes to thicken slightly.
Add mushrooms back. Return the sautéed mushrooms to the pan. Toss to coat and simmer 1 minute. Taste and season with salt, pepper, and a pinch of red pepper flakes if you like heat.
Finish with pasta. Add the drained pasta to the pan with 1/3–1/2 cup reserved pasta water.
Toss over low heat until the sauce clings to the pasta, 1–2 minutes.
Cheese and brightness. Off the heat, stir in Parmesan and lemon zest. If needed, add more pasta water to loosen. Adjust seasoning to taste.
Serve. Plate, then top with extra Parmesan and chopped parsley or chives.
Serve immediately while hot and glossy.