Season the chicken with salt and pepper. Heat oil or butter in a skillet over medium-high heat. Sear the chicken until golden and juices run clear, about 4–5 minutes per side. Remove and set aside.
In the same pan, add a touch more oil if needed. Sauté onions until translucent, then add garlic and mushrooms. Cook until mushrooms soften and start to brown, about 5–7 minutes.
Pour in chicken broth to deglaze the pan, scraping up all the tasty browned bits. Let it simmer for 2–3 minutes.
Stir in cream, Dijon mustard, and thyme. Bring to a gentle simmer and reduce slightly, 3–5 minutes, until the sauce thickens.
Return the chicken to the pan. Simmer a few minutes more until everything’s heated through and coated in that silky sauce. Stir in Parmesan if using. Taste and adjust salt and pepper.