Preheat oven to 350°F.
Heat olive oil in a large cast-iron skillet over medium-high heat.
Season chicken breasts with salt and pepper.
Place chicken in skillet spaced apart and sear until golden, about 3 minutes per side, then remove and set aside.
In the same skillet, sauté minced garlic, fresh thyme, and crushed red pepper flakes until fragrant, about 1 minute.
Add chicken broth, heavy cream, sun-dried tomatoes, and Parmesan cheese. Season lightly with salt and stir to combine.
Bring the sauce to a simmer.
Return chicken to the skillet, nestling it into the sauce.
Transfer skillet to the oven and bake for 15 minutes or until chicken reaches an internal temperature of 165°F.
Remove from oven, garnish with chopped fresh parsley, and serve immediately over your choice of pasta, rice, or mashed potatoes.