If the chicken breasts are thick, pound them to an even thickness of about 3/4 inch. Pat them dry, then season both sides with the divided kosher salt, black pepper, and Italian seasoning.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Sear the chicken for about 4–5 minutes per side until browned, then transfer it to a plate; it may not be fully cooked yet.

Add the remaining tablespoon of olive oil to the skillet. Cook the onion for 2–3 minutes, then add the garlic and optional red-pepper flakes and cook for about 30 seconds.

Pour in the chicken broth and scrape up the browned bits from the bottom of the pan. Simmer for 1–2 minutes so the broth absorbs the savory skillet flavor.

Reduce the heat to medium-low and stir in the heavy cream and Parmesan. Cook for 2–3 minutes, stirring, until the sauce begins to thicken without reaching a hard boil.

Add the fresh spinach and stir until it wilts, which takes about 1–2 minutes. If using thawed frozen spinach instead, heat it through after squeezing it very dry.

Return the chicken and any accumulated juices to the skillet. Cover and simmer gently for 5–8 minutes, until the thickest part of each breast reaches 165°F (74°C).

Sprinkle the optional mozzarella over the chicken and sauce. Cover for 1–2 minutes until the cheese melts, then garnish with parsley and serve.