Preheat the oven to 375°F. Trim any excess fat off of the chicken breasts then pat dry with a paper towel. Season the chicken generously on both sides with salt and pepper.
Heat skillet medium-high heat. the chicken breasts and cook for 3-4 minutes per side. The chicken will brown but it won't be fully cooked yet. Transfer the chicken to a clean plate and set aside.
Reduce the heat to medium-low. Allow the temperature to lower and add the garlic. Cook until fragrant, about 30 seconds. Stir in the broth then scrape any chicken bits stuck at the bottom of the pan.
Remove from the heat and let the pan cool slightly. Add the heavy cream and whisk to combine. Sprinkle in the parmesan cheese and stir until melted.
Return the pan to medium-low heat and continue to stir the sauce for approximately 1 minute. Add the sun-dried tomatoes, oregano, and red pepper flakes stir to combine, and adjust the seasoning as needed.
Once the sauce comes to a slow simmer, return the chicken to the skillet, coat with sauce, and transfer the skillet to the oven to continue cooking.
Bake for 12-15 minutes or until the internal temperature of the chicken reaches approximately 165°F. Remove the skillet from the oven. Spoon the sauce over the chicken and allow it to rest and cool for 5 minutes. Garnish with fresh basil and serve.
Notes
For a thicker sauce - Add more parmesan cheese, room-temperature cream cheese, or flour. Stir in after you take the skillet out of the oven.
Drain the oil from the sun-dried tomatoes before adding it to the sauce.