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 skillet and melt. Sauté chopped onions for 2 minutes until translucent. Add sliced mushrooms and cook for 4 to 5 minutes, stirring occasionally, until mushrooms are browned and moisture has evaporated. Add minced garlic and cook for 1 minute until fragrant.
04 - Pour in chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the skillet. Let the mixture simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream and fresh thyme leaves. Bring the sauce to a gentle simmer, stirring constantly to combine.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Simmer uncovered for 8 to 10 minutes until chicken is completely cooked through and sauce has thickened to desired consistency.
07 - Taste the sauce and adjust seasoning with additional salt and pepper if needed. Sprinkle with chopped fresh parsley and serve immediately.