Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through. Remove chicken from skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for 4-5 minutes until they release their moisture and start to brown.
Add the minced garlic to the mushrooms and cook for 1 minute until fragrant.
Pour in the chicken broth and stir, scraping up any browned bits from the bottom of the skillet.
Reduce heat to medium and stir in the heavy cream, Parmesan cheese, dried thyme, and crushed red pepper flakes.
Simmer the sauce for 3-4 minutes until it thickens slightly.
Stir in the butter until melted and the sauce is smooth.
Return the cooked chicken breasts to the skillet, spooning some sauce over the top.
Cook for an additional 2 minutes to heat the chicken through.
Garnish with chopped fresh parsley before serving.