Step 1: Heat olive oil and butter in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for 5-6 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.

Step 2: In the same skillet, add the chopped onion and garlic. Sauté for 2-3 minutes until softened and fragrant.

Step 3: Add the sliced mushrooms and cook for 5-7 minutes, until they are tender and browned.

Step 4: Pour in the chicken broth, scraping up any bits from the bottom of the skillet. Let the broth simmer for 2 minutes.

Step 5: Stir in the heavy cream and dried thyme. Return the chicken breasts to the skillet and simmer for 5-7 minutes, allowing the sauce to thicken and the chicken to absorb the flavors.

Step 6: Taste and adjust the seasoning with salt and pepper. Garnish with fresh parsley before serving.