Add elbow macaroni to a large pot of boiling water. Add the broccoli to the pot with about 5 minutes left in the pasta cooking process.
In a large skillet, melt butter. Add onion and chicken and cook over medium to low heat about 5 minutes. Add garlic, cook and stir for one minute.
Add flour and cook another minute, or until the flour is golden and well combined. Add half & half, milk and chicken stock. Stir constantly until the flour is completely incorporated into the liquid. Heat to medium heat, stirring occasionally as the mixture thickens. Season with salt and pepper.
Once the sauce is thick, turn to low and add cheese, mix well until cheese is melted. Add cooked macaroni and broccoli and mix well. Pour into a 9 x 11 baking dish prepped with cooking spray. Top with grated parmesan and bread crumbs. Spray a little more cooking spray on top.
Bake for 20 minutes. Allow to sit for 5 minutes before serving.