Season the chicken breasts evenly with salt and black pepper on both sides.
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 butter to the same skillet.
Once butter is melted, add sliced mushrooms and cook for 5 minutes until they release their moisture and begin to brown.
Add minced garlic to the mushrooms and cook for 1 minute until fragrant.
Pour in chicken broth, scraping the bottom of the skillet to deglaze and loosen any browned bits.
Stir in heavy cream, grated Parmesan cheese, dried thyme, and paprika. Simmer the sauce for 3-4 minutes until it thickens slightly.
Return the cooked chicken breasts to the skillet, spooning the creamy mushroom sauce over them.
Cook for an additional 2-3 minutes to heat the chicken through and allow flavors to meld.
Sprinkle chopped fresh parsley over the top before serving.