**Prepare the Chicken:** Season the chicken breasts with salt and pepper on both sides.
**Sear the Chicken:** Heat olive oil or butter in a large skillet over medium-high heat. Add the chicken breasts and cook for 4–5 minutes per side until golden brown. Remove chicken from the skillet and set aside.
**Cook the Mushrooms:** In the same skillet, add the sliced mushrooms. Cook for 4–5 minutes until softened and golden, stirring occasionally.
**Add Garlic:** Stir in the minced garlic and cook for 1 minute until fragrant.
**Make the Sauce:** Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Stir in the heavy cream, Parmesan cheese, and dried thyme. Simmer for 2–3 minutes until slightly thickened.
**Combine and Cook:** Return the chicken breasts to the skillet, spooning the sauce over them. Reduce heat to low, cover, and simmer for 10–12 minutes, or until the chicken is cooked through (internal temperature of 165°F/74°C).
**Garnish and Serve:** Sprinkle with fresh parsley before serving.