Prepare the chicken: Pat chicken breasts dry, season with salt and pepper, then dredge lightly in flour. Shake off excess.
Sear the chicken: Heat olive oil and butter in a large skillet over medium-high heat. Sear chicken 4–5 minutes per side until golden. Transfer to a plate.
Make the sauce: In the same pan, sauté garlic until fragrant. Add chicken broth and scrape brown bits. Stir in heavy cream, sun-dried tomatoes, Parmesan, Italian seasoning, and chili flakes. Simmer for 3–4 minutes until slightly thickened.
Combine chicken & sauce: Return chicken breasts to skillet, coat with sauce, and simmer 10 minutes until cooked through (internal temp 74°C).
Garnish & serve: Sprinkle with fresh basil leaves and serve warm.