Cook pasta as directed on package, adding broccoli to the boiling water for the last 2 minutes of the pasta cooking time. Drain pasta mixture.

Meanwhile, heat dressing in a large nonstick skillet on medium-high heat. Add chicken and cook until no longer pink in the center, stirring occasionally, about 5 to 7 minutes.

Stir in milk, cream cheese, Parmesan cheese, and basil. Bring to a boil, stirring constantly. Cook until sauce is well blended and heated through, about 1 to 2 minutes.