If the chicken breasts are thick, slice them horizontally or pound them to an even thickness. Pat them dry, then season both sides with the divided kosher salt, black pepper, and optional paprika.

Place the seasoned chicken in the flour and lightly coat each piece. Shake off excess flour so the coating stays thin and does not make the sauce heavy.

Heat a large skillet over medium-high heat, then add the olive oil and 1 tablespoon of the butter. Sear the chicken for about 4–5 minutes per side, until golden and nearly cooked through, then transfer it to a plate.

Reduce the heat to medium and add the remaining butter. Stir in the minced garlic and cook for 30–60 seconds, just until fragrant, taking care not to let it brown.

Pour in the chicken broth and scrape the browned bits from the bottom of the skillet. Let the broth simmer for 2–3 minutes so the pan juices become part of the sauce.

Stir in the heavy cream and optional Italian seasoning. Simmer gently for 3–5 minutes, until the sauce begins to thicken.

Add the finely grated Parmesan and stir over low heat until it melts into a smooth sauce. Avoid boiling at this stage, since high heat can make the dairy separate or turn grainy.

Return the chicken and any juices from the plate to the skillet. Spoon the sauce over the chicken and simmer gently for another 2–4 minutes.

Check that the thickest part of each chicken breast reaches 165°F (74°C) and that the sauce coats the back of a spoon. Finish with chopped parsley and an optional small squeeze of lemon juice before serving.