Cook pasta according to directions; drain. Set aside.
Season chicken with dried basil, salt, pepper, and garlic. Grill. Set aside.
Melt butter in a skillet. Add green onions and Italian seasoning. Saute for 5 minutes.
Add garlic and saute for 1 more minute. Stir in tomatoes, 3 tbsp. fresh basil, cream, milk, and hot pepper flakes. Bring to a boil, then reduce heat and simmer for 5 minutes.
Whisk in Parmesan until melted.
Serve pasta topped with chicken, then sauce, then a little more fresh basil.