Season both sides of the chicken breasts with kosher salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through. Remove chicken from skillet and set aside.
Reduce heat to medium and add minced garlic to the skillet. Sauté for about 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.
Stir in the heavy cream, grated Parmesan cheese, dried Italian seasoning, and crushed red pepper flakes. Cook, stirring frequently, until the sauce thickens slightly, about 3-4 minutes.
Add the unsalted butter to the sauce and stir until melted and combined.
Return the cooked chicken breasts to the skillet, spoon some sauce over the top, and simmer for an additional 2-3 minutes to heat through and meld flavors.
Sprinkle chopped fresh parsley over the chicken and sauce before serving.