Set the grill to medium high heat (or use a ribbed grill pan on the stovetop). Spray with cooking spray.
Season the chicken with the salt and pepper. Place on the grill and cook for approximately 10 minutes - until the juices run clear. Remove from grill and let stand for five minutes. Cut chicken into bite-sized pieces; keep warm.
Cook pasta according to package directions. Drain in a colander placed over a bowl. Save 1/2 cup of the cooking liquid. Place the drained pasta into a large serving bowl.
Heat butter in a medium saucepan over medium heat. Add the garlic and cook one minute, stirring occasionally.
Combine the 1/2 cup milk and flour in a small bowl. Whisk until smooth. Add this mixture to the garlic and butter whisking constantly. Stir in the pesto. Slowly add the remaining milk - whisking constantly. Cook, stirring frequently, for 8 minutes or until the sauce thickens.
Add the reserved cooking liquid and one cup of the shredded cheese, stir until the cheese melts. Add salt and pepper if desired.
Add the chicken and the sauce to the bowl of pasta, tossing well to coat. Add the tomatoes and basil and gently toss again. Sprinkle with the remaining cheese and serve immediately.