Pat the chicken breasts dry with paper towels. Season both sides with salt, black pepper, and paprika.
In a large skillet over medium heat, melt 2 tablespoons of butter. Add the chicken breasts and cook for 5-7 minutes per side, or until golden brown and cooked through (internal temperature should reach 165°F). Remove chicken from skillet and set aside on a plate.
In the same skillet, reduce heat to medium-low and add the remaining 1 tablespoon of butter. Add the minced garlic and sauté for 1 minute until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth and use a wooden spoon to scrape up any browned bits from the bottom of the skillet. Let it simmer for 2 minutes.
Stir in the heavy cream, grated Parmesan cheese, and dried Italian seasoning. Cook, stirring frequently, until the sauce thickens slightly, about 3-4 minutes.
Return the cooked chicken breasts to the skillet and spoon the sauce over them. Let them simmer in the sauce for 2-3 minutes to heat through and absorb flavors.
Sprinkle chopped fresh parsley over the chicken and sauce before serving.