In a pan cook chopped chicken with garlic and other seasonings you like. (I used a little Jamaican Jerk seasoning.).
Prepare the white sauce. Place butter in small saucepan (preheated) over medium heat. Once the butter foams, add flour and stir for 1 minute (try not to let it turn brown). Add milk to the mix and continue stirring until it starts to bubble. Reduce heat; simmer for 10 minutes. Add and stir in pepper, Italian seasoning, and parmesan cheese.
While white sauce is simmering, boil water for penne. Cook penne about 8-9 minutes and for the last minute add the chopped broccoli.
In a large bowl, combine pasta, broccoli, chicken and chopped veggies. Stir white sauce inches Pour all into a large casserole dish. Sprinkle on cheese. Cover with foil or lid. Bake for 20-30 minutes.