Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Reserve ½ cup pasta water and drain.
In a large skillet, heat olive oil over medium-high heat. Season chicken with salt and pepper, then cook for 5–6 minutes until golden and cooked through. Transfer to a plate and set aside.
In the same pan, lower heat to medium. Add a touch more oil if needed, then sauté garlic for 1 minute. Add sun-dried tomatoes, Italian seasoning, and red pepper flakes. Cook for 2–3 minutes until fragrant.
Pour in the chicken broth and bring to a simmer. Stir in heavy cream and Parmesan cheese. Simmer for 3–5 minutes until sauce slightly thickens.
Return the chicken to the skillet and add cooked pasta. Toss to coat everything evenly. If the sauce is too thick, add a splash of reserved pasta water.
Stir in fresh basil and adjust seasoning with salt and pepper. Serve immediately with extra Parmesan if desired.