Prepare the chicken. Pat chicken breasts dry with paper towels and season generously with salt and pepper on both sides.
Sear the chicken. In a large skillet, heat olive oil and butter over medium-high heat. Add chicken and sear for 4–5 minutes per side, until golden brown. Remove chicken and set aside.
Build the sauce base. In the same skillet, add garlic and cook for 30 seconds until fragrant. Pour in chicken broth and use a wooden spoon to scrape up any browned bits.
Add the cream and cheese. Lower the heat to medium. Stir in heavy cream, Parmesan, oregano, thyme, and red pepper flakes. Simmer for 3–4 minutes until the sauce begins to thicken.
Incorporate sun-dried tomatoes. Stir them into the sauce, letting their flavor infuse for another 2 minutes.
Finish cooking the chicken. Return chicken breasts to the skillet, nestling them into the sauce. Simmer for 8–10 minutes, or until chicken reaches 165°F internal temperature.
Garnish and serve. Sprinkle with fresh basil or parsley, and serve hot with your favorite sides.