Slice chicken breasts into thin cutlets, pat dry, season with salt and pepper, and dredge in flour. Shake off excess.
Heat olive oil and butter in a large skillet over medium heat. Cook chicken 4 minutes per side until golden and cooked through. Remove and set aside.
Lower heat slightly, add garlic (and a spoonful of sun‑dried tomato oil if available) to the skillet and sauté until fragrant.
Pour in chicken stock and scrape up browned bits with a wooden spoon.
Reduce heat to low. Stir in heavy cream and Parmesan cheese until sauce is smooth and thickened.
Add sun‑dried tomatoes or paste, dried thyme, oregano, and chili flakes. Stir to combine.
Return chicken to the skillet, spoon sauce over each piece, and simmer a few minutes until sauce thickens and clings.
Turn off heat, garnish with chopped fresh basil, and serve immediately with your choice of sides.