In a large soup pot, cook noodles according to package. Add the asparagus to the boiling noodles once there is 3 minutes left to cook. Drain noodles and asparagus. Rinse with cool water. This will stop the noodles and asparagus from cooking.
While the noodles are cooking take a large skillet and warm to medium heat. Add the butter and melt. Once butter is melted, add the garlic and sauté, about 30 seconds. Sprinkle flour over garlic, making sure to stir constantly until it becomes a light golden color, about 2 minutes.
Slowly add the half and half and chicken broth. Make sure to only add 1 cup at a time and make sure to stir constantly. This will avoid any lumps in your sauce.
Bring the sauce to a simmer and cook until slightly thickened, about 4-5 minutes. Stir in the Parmesan cheese, salt and pepper.
Pour sauce over noodles, asparagus and cubed chicken. You might have some extra sauce. That's ok. You can save it and use it on the leftover pasta, or freeze it for a later time. Toss the pasta lightly to combine.
Serve immediately and enjoy.