Heat a large pot over medium heat and add the ground beef. Cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion, minced garlic, and grated ginger to the pot. Stir and cook for 2 minutes until the onion softens.
Stir in the sliced carrots and shredded cabbage. Cook for another 3 minutes to let the vegetables start to wilt.
Pour in the beef broth and soy sauce. Bring the soup to a simmer and cook for 10 minutes.
Remove the pot from the heat and stir in the sesame oil. Taste and add salt and pepper as needed.
Ladle the soup into bowls and top each serving with sliced green onions.