In a large pot over medium heat saute the onion and garlic in the butter for 2-3 minutes until tender. Whisk in the flour and cook whisking constantly for 2 minutes until bubbly.
Whisk in the chicken stock.
Once the stock is simmering add the egg noodles and cook for 8-10 minutes until noodles are tender.
Stir in the heavy cream, parmesan cheese, cooked broccoli, salt, pepper, and chicken.
Allow the soup to cook for 2-3 more minutes until everything is heated through.
What I do to keep that super easy is purchase the frozen broccoli that you can steam right in the bag. It usually takes about 4-5 minutes in the microwave and you can get that going in a snap while your noodles cook. For the pasta, I recommend using egg noodles for one reason, they cook fast! This way your pasta cooks quickly and you still have plenty of liquid for your soup!