Season the chicken breasts with salt and black pepper on both sides. Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for about 6-7 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for about 5 minutes, or until they are browned and tender. Add the minced garlic and cook for an additional 1 minute, stirring frequently.
Pour in the chicken broth and heavy cream, stirring to combine. Add the dried thyme and paprika. Bring the mixture to a gentle simmer, then reduce the heat to low.
Stir in the grated Parmesan cheese until melted and the sauce is creamy. Return the chicken to the skillet, spooning the sauce over the top. Let it simmer for another 2-3 minutes to heat the chicken through.
Garnish with fresh parsley before serving.