Season both sides of the chicken breasts with salt and black pepper.
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, 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 prevent burning.
Pour in the chicken broth and use a wooden spoon to scrape 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. Bring the mixture to a gentle simmer and cook for 3-4 minutes until the sauce thickens slightly.
Add the unsalted butter to the sauce and stir until melted and incorporated.
Return the cooked chicken breasts to the skillet, spooning some sauce over the top. Simmer for an additional 2-3 minutes to heat the chicken through and meld the flavors.
Sprinkle chopped fresh parsley over the chicken and sauce before serving.