01 - Pat chicken breasts dry with paper towels. Season both sides evenly with salt and black pepper. Lightly dredge each breast in flour, coating completely, then shake off excess flour.
02 - Heat olive oil in large skillet over medium-high heat until shimmering. Place chicken breasts in skillet and cook for 5 to 6 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to plate and cover loosely with foil.
03 - Reduce heat to medium. Add butter to same skillet and melt. Add sliced mushrooms and sauté for 5 to 6 minutes, stirring occasionally, until golden brown and moisture has evaporated.
04 - Add minced garlic and fresh thyme to skillet. Cook for 1 minute, stirring constantly, until fragrant but not browned.
05 - Pour in chicken broth, using wooden spoon to scrape up browned bits from bottom of skillet. Simmer for 2 minutes until slightly reduced.
06 - Stir in heavy cream and grated Parmesan cheese. Simmer for 2 to 3 minutes, stirring occasionally, until sauce coats back of spoon and thickens slightly.
07 - Return chicken breasts to skillet, spooning sauce over each piece. Simmer for 2 to 3 minutes until chicken is heated through. Garnish with chopped fresh parsley before serving.