Add the beef stew meat, beef broth, soy sauce, minced ginger, minced garlic, sliced onion, and sliced carrots to the slow cooker.
Stir the ingredients together, cover, and cook on low for 7 to 8 hours until the beef is very tender.
About 20 minutes before serving, cook the egg noodles in a separate pot according to package directions until just tender, then drain.
Stir the cooked noodles into the slow cooker along with the sesame oil.
Ladle the soup into bowls and top each serving with sliced green onions.