Season both sides of the chicken breasts with 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 until golden brown and cooked through. Remove chicken from skillet and set aside.
Reduce heat to medium and add the minced garlic to the skillet. Sauté for 1 minute until fragrant.
Pour in the chicken broth and scrape the bottom of the skillet to loosen any browned bits.
Stir in the heavy cream, Parmesan cheese, dried Italian seasoning, and crushed red pepper flakes. Cook for 3-4 minutes, stirring frequently, until the sauce thickens slightly.
Add the butter to the sauce and stir until melted and incorporated.
Return the cooked chicken breasts to the skillet, spoon some sauce over them, and cook for an additional 2 minutes to heat through.
Sprinkle chopped fresh parsley over the skillet before serving.