Pat chicken breasts completely dry with paper towels. Season both sides with 1/2 teaspoon salt and black pepper. Place flour in a shallow dish and lightly dredge each chicken breast, shaking off excess. Let rest for 5 minutes.

Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Once oil shimmers and begins to smoke, add chicken breasts. Cook undisturbed for 4-5 minutes per side until golden and internal temperature reaches 165°F. Remove to a plate and tent with foil.

Reduce heat to medium. Add remaining 1 tablespoon olive oil and butter to the skillet. Add minced garlic and sauté for 30 seconds until fragrant. Stir in sun-dried tomatoes, Italian seasoning, and red pepper flakes. Cook for 1 minute.

Pour in chicken broth to deglaze, scraping up brown bits from the bottom. Simmer for 2 minutes to reduce slightly. Add heavy cream and bring to a gentle simmer.

Stir in parmesan cheese and continue stirring until melted and sauce is smooth, about 2-3 minutes. Return chicken and juices to the skillet. Spoon sauce over chicken and simmer for 3-4 minutes until heated through and sauce thickens.

Taste and adjust seasoning with remaining salt if needed. Garnish with fresh torn basil leaves before serving.