1. Heat olive oil and butter in a large skillet over medium heat. Sear chicken breasts on both sides until golden brown, about 4-5 minutes per side. Remove and set aside.
2. In the same skillet, sauté onions (if using) and garlic until fragrant. Add mushrooms and cook until golden and tender.
3. Stir in chicken broth, scraping up any browned bits. Let it simmer for 2 minutes, then pour in the heavy cream and thyme. Season with salt and pepper to taste.
4. Return the chicken breasts to the skillet, spoon the sauce over them, and simmer for 8-10 minutes, or until the chicken is fully cooked (internal temp: 165°F).
5. Serve hot, garnished with fresh parsley. Pair with rice, mashed potatoes, or pasta for a complete meal.