Preheat oven to 375°F. Pat chicken dry and season with salt and pepper.
Heat oil in cast iron skillet over medium-high heat, covering entire surface. Sear chicken 3-4 minutes on each side. Remove chicken from skillet and set aside.
Reduce heat to medium-low, add garlic, and sauté 1 minute. Add broth and stir, scraping up any browned bits.
Remove skillet from burner and cool slightly before adding cream. Whisk cream into chicken broth. Sprinkle Parmesan into mixture and stir until cheese has melted.
Return skillet to hot burner and continue stirring 1 minute until heated. Add sun-dried tomatoes, oregano, and red pepper; stir gently until mixed well.
Bring sauce to slow simmer, stirring occasionally. Return chicken to skillet, coat in sauce, and bake for 12-15 minutes until internal temperature reaches 162°F.
Remove skillet from oven; set aside. Spoon sauce over chicken, then let rest 5 minutes. Chicken will continue to cook to reach 165°F. Serve with sauce and top with basil.