01 - Pat chicken breasts dry with paper towels. Season both sides generously with salt and pepper.
02 - Heat olive oil in a large skillet over medium-high heat. Add chicken breasts and cook 5 to 6 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil.
03 - In the same skillet, add mushrooms and onion. Sauté 4 to 5 minutes until softened and browned. Add garlic and cook 1 minute, stirring constantly to prevent burning.
04 - Pour chicken broth into the skillet, scraping up any browned bits from the bottom. Simmer 2 minutes until slightly reduced.
05 - Reduce heat to medium. Stir in heavy cream, Dijon mustard, thyme, and Parmesan cheese. Simmer 2 to 3 minutes, stirring occasionally, until sauce thickens enough to coat a spoon.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Spoon sauce over the chicken and simmer 2 to 3 minutes until heated through.
07 - Sprinkle with fresh parsley if desired. Serve hot with rice, mashed potatoes, or crusty bread to soak up the sauce.