Roast garlic and broccoli florets for 30 minutes at 450 degrees F until fork tender.
Cook chicken and chop. You may use a rotisserie chicken, boil, broil or bake chicken.
Cook pasta according to package directions to al dente stage. Drain.
Melt butter in a large skillet or saute pan. Add flour, whisk and cook 1 minutes until lightly brown.
Stir in chicken broth, milk, and heavy cream. Whisk constantly for 2 to 3 minutes until well incorporated, there are no lumps and the mixture begins to thicken.
Add Parmesan and stir until cheese melts for about 1 minute.
Add pasta, chicken, and broccoli and stir to coat all with white sauce.