Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1 cup of pasta water, then drain pasta and set aside.
In a large skillet over medium heat, add olive oil. Season the chicken pieces with salt and pepper, then add to the skillet. Sauté until golden and cooked through, about 6-8 minutes. Remove chicken from skillet and set aside.
In the same skillet, add a small amount of additional olive oil if needed. Add the minced garlic and cook until fragrant, about 30 seconds to 1 minute. Then add chicken broth, bringing it to a simmer and scraping up any browned bits. Stir in heavy cream, Parmesan cheese, sun-dried tomatoes, oregano, thyme, and red pepper flakes.
Return the cooked chicken to the skillet and let the sauce simmer for a few minutes until it begins to thicken. Add the pasta, stirring to coat it evenly in the sauce. If needed, add reserved pasta water, a little at a time, until the sauce reaches your desired consistency.
Garnish with fresh basil and additional grated Parmesan. Serve immediately and enjoy!
