Season the chicken breasts with salt and pepper on both sides. For even cooking, pound them to an even thickness of about ¾ inch. If your chicken breasts are particularly large, consider cutting them in half horizontally.
Heat olive oil in a large skillet over medium-high heat. Once hot, add the chicken breasts and cook for 5-6 minutes per side until golden brown and nearly cooked through (internal temperature around 155°F).
Remove the chicken from the skillet and set aside. In the same pan, add the minced garlic and sauté for 30 seconds until fragrant. Be careful not to burn it, as garlic becomes bitter when overcooked.
Pour in the chicken broth and scrape the bottom of the pan to release any browned bits. Add the heavy cream, chopped sun-dried tomatoes, dried oregano, and red pepper flakes. Bring to a gentle simmer.
Reduce the heat to medium-low and stir in the Parmesan cheese until melted and incorporated. Return the chicken to the skillet, spooning the sauce over the top. Simmer for 3-5 minutes until the chicken is completely cooked through (165°F) and the sauce has slightly thickened.
Garnish with fresh basil leaves and serve with your choice of pasta, rice, or bread to soak up the delicious sauce.