Cook the pasta: Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente.
Reserve 1 cup of pasta water, then drain and set aside.
Season the chicken: Pat dry and season all over with salt, pepper, and half the Italian seasoning.
Sear the chicken: Heat olive oil and butter in a large skillet over medium-high. Add chicken in a single layer. Cook 3–4 minutes per side until golden and cooked through.
Transfer to a plate and tent loosely with foil.
Sauté aromatics: Lower heat to medium. Add garlic and red pepper flakes. Stir 30 seconds until fragrant, scraping up browned bits.
Build the sauce: Add sun-dried tomatoes and the remaining Italian seasoning.
Stir for 1 minute. Pour in chicken broth and simmer 2–3 minutes to reduce slightly.
Add cream and cheese: Stir in heavy cream and bring to a gentle simmer. Whisk in Parmesan a handful at a time until smooth.
If the sauce gets too thick, add a splash of broth or reserved pasta water.
Combine: Slice or cube the chicken if needed. Add chicken and any juices back to the skillet. Stir in chopped basil.
Taste and adjust salt, pepper, and heat. Add lemon juice if you want extra brightness.
Toss with pasta: Add the cooked pasta to the skillet and toss until coated. Use reserved pasta water, a few tablespoons at a time, to loosen and help the sauce cling.
Finish and serve: Top with more Parmesan and basil.
Serve hot.