01 - Pat chicken breasts dry and season both sides with salt and black pepper.
02 - Warm olive oil and unsalted butter in a large skillet over medium-high heat.
03 - Place chicken breasts in the skillet and sear for 5 to 6 minutes per side until golden brown and fully cooked. Remove and set aside.
04 - Add chopped onion to the same skillet and sauté for 2 minutes until translucent.
05 - Add sliced mushrooms and cook for 4 to 5 minutes until browned and liquid has evaporated.
06 - Stir in minced garlic and dried thyme; cook for 1 minute until fragrant.
07 - Pour in chicken broth, scraping up browned bits from the pan, and simmer for 2 minutes.
08 - Reduce heat to medium-low, then add heavy cream and grated Parmesan cheese, stirring continuously until the sauce thickens, about 2 to 3 minutes.
09 - Return chicken breasts to the skillet, spoon sauce over them, and simmer gently for 3 to 5 minutes until heated through.
10 - Sprinkle with fresh parsley and serve immediately while hot.