Season both sides of the chicken breasts with salt, black pepper, and paprika.
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.
Reduce heat to medium and add the butter to the same skillet.
Add the minced garlic and sliced mushrooms to the skillet and sauté for 4-5 minutes until the mushrooms are tender and browned.
Pour in the chicken broth and use a wooden spoon to scrape any browned bits from the bottom of the skillet.
Stir in the heavy cream, Parmesan cheese, and dried thyme. Cook for 3-4 minutes, stirring occasionally, until the sauce thickens slightly.
Return the cooked chicken breasts to the skillet and spoon the sauce over them.
Simmer for an additional 2-3 minutes to heat the chicken through and meld the flavors.
Sprinkle chopped fresh parsley over the top before serving.