In a large pot over medium-high heat, add the ground pork. Cook for 5-7 minutes, using a spatula to break it apart, until the pork is browned and cooked through. Drain any excess fat from the pot.

Lower the heat to medium and add the diced onion, minced garlic, and grated ginger to the pot with the browned pork. Sauté for 3-4 minutes until the onions become translucent.

Pour in the soy sauce, sesame oil, and rice vinegar, stirring to combine. Slowly add the low-sodium chicken broth, bringing the mixture to a gentle boil over high heat.

Once boiling, incorporate the shredded carrots and thinly sliced green cabbage into the pot. Reduce heat and cover, cooking for about 15 minutes.

If using, slowly drizzle beaten eggs into the soup while gently stirring. Allow it to cook for an additional minute to set the eggs.

Taste the soup and adjust seasoning with salt and pepper. Ladle the soup into bowls, garnishing with reserved chopped green onions.