1. Bring a large pot of well-salted water to a boil and cook the pasta until just under al dente. Reserve about 1/2 cup pasta water, then drain pasta and set aside.
2. Meanwhile, season chicken thighs with salt and pepper. Optionally, dust with flour. Heat 1 tablespoon olive oil in a skillet over medium-high heat. Sear chicken until golden brown (4-5 minutes per side if whole). Remove and set aside.
3. In the same skillet, add butter and remaining olive oil. Sauté onions and garlic until fragrant, about 2-3 minutes. Add mushrooms and cook until tender, about 5-6 minutes.
4. Add rosemary or thyme, cooking for 1 minute. Add white wine and reduce by half (2-3 minutes). Add chicken stock and cream, stirring to combine. Thicken with cornstarch if needed.
5. Gradually stir in parmesan cheese in two batches, melting fully. Season with salt, pepper, and lemon juice.
6. Slice chicken and return to the skillet. Add pasta, tossing to coat with sauce. Simmer for 1-2 minutes, adding pasta water as needed.
7. Stir in parsley and serve with lemon zest and extra parmesan.