Season both sides of the chicken breasts with salt and pepper.
Heat olive oil in a large non-stick skillet over medium-high heat. Add the chicken breasts and cook for about 10 minutes on each side, or until golden brown. Remove the chicken from the skillet and set aside.
Using the same skillet, add the chopped sun-dried tomatoes and minced garlic. Cook for about 2 minutes, stirring occasionally, until fragrant.
Sprinkle in the dried basil, oregano, and thyme. Stir and let cook for an additional 30 seconds to release their aroma.
Pour in the chicken broth and bring the mixture to a simmer. Let it cook for 5 minutes, allowing the liquid to reduce slightly.
Lower the heat to a gentle simmer and pour in the heavy cream. Add the grated Parmesan cheese and stir until the cheese is melted and the sauce is smooth.
Return the chicken breasts to the skillet, ensuring they are well coated with the sauce. Cover the skillet and simmer for 10-12 minutes, or until the chicken is fully cooked and the sauce has thickened.
Sprinkle chopped fresh parsley over the dish before serving for a bright, flavorful garnish.