If the chicken breasts are very thick, slice them horizontally into cutlets or pound them to an even thickness. Season both sides with the kosher salt and black pepper, then lightly dredge each breast in flour and shake off the excess.

Heat the olive oil and unsalted butter in a large skillet over medium-high heat. Sear the chicken for approximately 4–5 minutes per side, until golden brown, then transfer it to a plate; it does not need to be fully cooked yet.

Reduce the heat to medium and add the minced garlic, crushed red pepper flakes, and Italian seasoning. Cook for about 30 seconds, stirring constantly and taking care not to let the garlic brown.

Pour the chicken broth into the skillet and scrape up the browned bits from the bottom. Simmer for 1–2 minutes so the broth picks up the savory flavor left by the seared chicken.

Stir in the heavy cream, Parmesan cheese, and chopped sun-dried tomatoes. Simmer gently for 3–5 minutes, stirring until the sauce thickens slightly, and avoid a vigorous boil so the cream remains smooth.

Return the chicken and any accumulated juices to the skillet. Spoon the sauce over the chicken, cover loosely, and simmer for approximately 5–8 minutes, or until the thickest part of the chicken reaches 165°F (74°C).

Stir in the chopped fresh basil or scatter it over the finished chicken. Add more basil for serving and bring the skillet to the table with your chosen pasta, potatoes, rice, or bread.