Preheat oven to 375° Fahrenheit. Liberally season each chicken breast with salt and pepper on both sides.
Heat olive oil in cast iron skillet over medium-high heat. When hot, add chicken to skillet. Sear 3 to 4 minutes, then flip and sear on other side 3 to 4 minutes.
Remove seared chicken from skillet and set aside. Add garlic to skillet and cook until fragrant, approximately 1 to 2 minutes.
Stir in broth and heavy cream, then slowly add grated parmesan, sun dried tomatoes, oregano, and red pepper flakes.
Bring mixture to simmer, then return chicken breasts to skillet. Quickly flip chicken a time or two to coat in sauce, then transfer entire skillet to oven.
Bake 15 to 20 minutes, or until chicken reaches internal temperature of 165° Fahrenheit.
Remove chicken from skillet and plate with desired sides. Spoon additional sauce from skillet over chicken, garnish with chiffonade basil, and serve immediately.