In a large skillet, cook sausage slices over medium heat until browned. Remove and set aside.
In the same skillet, sauté broccoli in a bit of olive oil until tender.
Add beef broth, heavy cream, egg noodles, garlic powder, onion powder, salt, and pepper. Bring to a boil.
Reduce heat and simmer, covered, for 10-12 minutes, or until noodles are cooked.
Stir in cooked sausage and shredded cheddar cheese until melted. Serve hot.