01 - Pat chicken breasts thoroughly dry with paper towels. Season both sides generously with salt and black pepper. Dust chicken lightly with flour, coating evenly and shaking off excess.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. Place chicken breasts in hot pan and sear for 4 to 5 minutes per side until deep golden brown and cooked through. Transfer chicken to a plate and set aside.
03 - Reduce heat to medium. Add butter to the same skillet and melt. Add sliced mushrooms and chopped onion, sautéing for 5 minutes until softened and lightly golden. Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
04 - Pour in chicken broth, using a wooden spoon to scrape up browned bits from the bottom of the pan. Let mixture simmer for 2 minutes until slightly reduced.
05 - Stir in heavy cream, grated Parmesan cheese, and dried thyme. Bring sauce to a gentle simmer, stirring constantly until cheese melts and sauce begins to thicken slightly.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Simmer uncovered for 7 to 10 minutes until chicken is cooked through and sauce has reached desired consistency. Baste chicken occasionally with sauce.
07 - Transfer chicken and sauce to serving plates. Garnish generously with fresh chopped parsley. Serve immediately over pasta, mashed potatoes, or steamed rice.