01 - Pat chicken breasts dry with paper towels. Season both sides generously with salt and black pepper. Lightly dust each breast with flour, shaking off excess.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken breasts and sear for 4 to 5 minutes per side until golden brown and cooked through. Transfer 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 golden.
04 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
05 - Pour in chicken broth, using a wooden spoon to scrape up browned bits from the bottom of the skillet. Let simmer for 2 minutes until slightly reduced.
06 - Stir in heavy cream, grated Parmesan cheese, and dried thyme. Bring to a gentle simmer, stirring constantly until cheese is melted and sauce begins to thicken.
07 - 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 reaches desired consistency. Sprinkle with fresh parsley and serve immediately.