Preparation of Oven and Chicken: Preheat the oven to 375 degrees Fahrenheit. In a large ovenproof skillet, heat one tablespoon of olive oil over medium-high heat. Season the chicken breasts liberally with kosher salt and freshly ground black pepper. Place the chicken in the skillet and cook until golden brown, approximately 5 minutes per side. Once browned, transfer the chicken breasts to a separate plate.
Sauce Creation: In the same skillet, reduce the heat to medium and add the remaining two tablespoons of olive oil. Introduce the minced garlic, fresh thyme leaves, and red pepper flakes to the skillet. Stir continuously and cook until the mixture becomes fragrant, about 1 minute. Subsequently, add the chicken broth, chopped sun-dried tomatoes, heavy cream, and grated Parmesan cheese to the skillet. Season with additional kosher salt to taste. Bring the mixture to a simmer, stirring occasionally.
Combining and Baking: Return the chicken breasts along with any accumulated juices to the skillet. Ensure that the chicken is well-coated with the sauce. Transfer the skillet to the preheated oven and bake until the chicken is thoroughly cooked and the juices run clear when pierced with a knife, about 10 to 12 minutes.
Final Presentation: Arrange the cooked chicken breasts on a serving platter. Spoon the creamy sauce generously over the chicken. Garnish with torn fresh basil leaves just before serving to add a fresh, aromatic touch to the dish.