Heat the oil in a skillet over medium-high heat. Add the chicken breasts and cook about 5 minutes per side until lightly golden and cooked through. Set aside to rest, keeping the juices in the pan for flavor.
In the same skillet, add chopped garlic and red pepper flakes. Sauté until fragrant, around 1 minute. Deglaze the pan with white wine or chicken broth to lift all the flavorful bits from the bottom.
Add the chicken broth, heavy cream, chopped sundried tomatoes, and grated Parmesan. Bring to a gentle boil, then reduce heat and simmer 3–5 minutes until the sauce thickens slightly.
Return the chicken to the pan with any resting juices. Stir in the fresh basil and season with salt and pepper. Allow the flavors to meld for another minute before serving.