Prepare Chicken:Pound chicken breasts to even thickness if needed. In a shallow bowl, combine flour, salt, and pepper. Dredge each chicken breast lightly in the flour mixture, shaking off any excess.
Cook Chicken:In a large skillet over medium heat, melt butter and olive oil together. Add chicken breasts and cook for 4-5 minutes per side until golden brown and cooked through. Remove chicken from skillet and set aside.
Make Sauce:In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant. Pour in chicken broth and stir, scraping up any browned bits from the pan.
Add Cream & Cheese:Reduce heat to low and stir in heavy cream and Parmesan cheese. Cook, stirring frequently, until sauce thickens slightly—about 3-4 minutes.
Add Basil:Stir in chopped fresh basil and red pepper flakes (if using).
Combine:Return chicken breasts to the skillet, spooning the sauce over them. Simmer for another 2-3 minutes until heated through.
Serve:Garnish with extra fresh basil and Parmesan, and serve hot with pasta, rice, or steamed vegetables.