Heat sundried tomato oil in a large skillet over medium-high heat. Cut the raw chicken breast into bite-sized pieces. Season the chicken with oregano, thyme, basil, salt, and pepper. Cook for 7-8 minutes until golden brown and cooked through. Remove the chicken, but leave the pan drippings for extra flavor.
To the pan drippings, add minced onion, minced garlic, and sun-dried tomatoes. Scrape the bottom of the pan to loosen any flavorful bits, and let the mixture simmer on low heat for 2-3 minutes until softened and fragrant.
Pour in chicken broth and stir in the penne pasta. Allow it to simmer for 10 minutes or until the pasta is al dente. Stir occasionally to prevent sticking.
Turn the heat to low, pour in the heavy cream, and add back in the cooked chicken. Stir in freshly grated Parmesan cheese until the sauce is smooth and creamy. Adjust seasoning with additional salt and black pepper if needed.
Let the dish sit for 5 minutes to allow the pasta to absorb the sauce. Then, garnish with additional Parmesan cheese and fresh basil. Serve hot and enjoy!