Pat the chicken thighs dry with paper towels. Season both sides with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Place the chicken thighs skin-side down and cook for 6-7 minutes until the skin is golden brown and crispy.
Flip the chicken thighs and cook for an additional 5 minutes. Remove the chicken from the skillet and set aside.
Reduce heat to medium and add the butter to the skillet. Once melted, add the sliced mushrooms and cook for 5 minutes until they release their moisture and begin to brown.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth, scraping the bottom of the skillet to loosen any browned bits. Let it simmer for 2 minutes.
Stir in the heavy cream, Parmesan cheese, and dried thyme. Cook for 3-4 minutes until the sauce starts to thicken.
Return the chicken thighs to the skillet, skin-side up. Spoon some sauce over the chicken.
Cover the skillet and reduce heat to low. Simmer for 10 minutes until the chicken is cooked through and the sauce is creamy.
Sprinkle chopped fresh parsley over the dish before serving.