01 - Pat chicken breasts dry with paper towels and season both sides generously with salt and black pepper.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken breasts and cook for 5 to 6 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and tent loosely with foil.
03 - In the same skillet, add sliced mushrooms and chopped onion. Sauté for 4 to 5 minutes until softened and lightly browned. Add minced garlic and cook for 1 minute, stirring constantly to prevent burning.
04 - Pour chicken broth into the skillet, scraping up any browned bits from the bottom with a wooden spoon. Let simmer for 2 minutes until slightly reduced.
05 - Reduce heat to medium. Stir in heavy cream, Dijon mustard, fresh thyme, and grated Parmesan cheese. Simmer for 2 to 3 minutes, stirring occasionally, until sauce thickens enough to coat the back of a spoon.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Spoon sauce generously over the chicken and simmer for 2 to 3 minutes until heated through.
07 - Sprinkle with fresh chopped parsley if desired. Serve immediately with rice, mashed potatoes, or crusty bread to soak up the sauce.