In a large pot, heat 2 tablespoons of olive oil over medium-high heat. Add 1 pound of ground pork, breaking it apart with a wooden spoon. Sauté for about 5-7 minutes, or until the pork is browned and cooked through.

Next, add 1 diced yellow onion, 3 cloves of minced garlic, and 1 tablespoon of grated fresh ginger to the pot. Sauté for 3-4 minutes until the onions become translucent.

Stir in 1/4 cup of soy sauce, 1 tablespoon of sesame oil, and 2 tablespoons of rice vinegar. Pour in 4 cups of low-sodium chicken broth and bring to a gentle boil.

Once the broth reaches a boil, add 1 cup of shredded carrots and 4 cups of thinly sliced green cabbage. Reduce the heat to low and let simmer uncovered for about 15 minutes.

If desired, slowly drizzle in 2 beaten eggs while stirring gently. Cook for an additional 1-2 minutes.

Taste the soup and adjust seasoning with salt and pepper as needed. Ladle into bowls and top with chopped green onions.