Season the chicken on both sides with Italian seasoning, salt, and pepper.
Heat the olive oil in a large skillet over medium-high heat. Cook the chicken for 4–5 minutes per side, until golden and cooked through (165°F). Transfer to a plate.
Reduce the heat to medium. Melt the butter in the skillet, add the garlic, and cook 1 minute, until fragrant.
Pour in the broth, scraping up the browned bits, and simmer 2 minutes.
Stir in the cream and Parmesan and simmer 3–4 minutes, until slightly thickened.
Return the chicken and any juices to the pan and spoon the sauce over it. Simmer 1–2 minutes, garnish with parsley, and serve.