01 - In a large pot over medium heat, add the ground beef. Cook until browned, breaking it apart with a spoon. Drain excess fat if necessary.
02 - Add diced onion, garlic, and ginger to the pot. Sauté for 2-3 minutes until fragrant and the onions are translucent.
03 - Stir in the julienned carrot and shredded cabbage. Cook for another 3-4 minutes until the vegetables begin to soften.
04 - Pour in the beef broth, soy sauce, rice vinegar, hoisin sauce (if using), sesame oil, and black pepper. Bring the soup to a gentle boil, then reduce heat and let simmer for 15 minutes to develop the flavors.
05 - Meanwhile, in a skillet, heat vegetable oil over medium-high heat. Fry the egg roll wrapper strips in batches until golden and crispy, about 30-60 seconds per side. Drain on paper towels.
06 - Taste the soup and adjust seasoning with additional soy sauce, salt, or pepper as needed.
07 - Ladle the soup into bowls and top with crispy egg roll strips, sliced green onions, and sesame seeds if desired. Serve immediately while hot.