Heat the sesame oil in a large pot over medium heat. Add the ground pork and cook, breaking it up with a spoon, until it is no longer pink.
Stir in the minced garlic and ginger. Cook for one minute until fragrant.
Add the sliced mushrooms and cook for three minutes until they begin to soften.
Pour in the chicken broth and soy sauce. Bring the mixture to a simmer.
Add the shredded cabbage and stir to combine. Simmer for eight to ten minutes until the cabbage is tender but still has some bite.
Taste and add salt and black pepper as needed. Remove from heat.
Ladle into bowls and top each serving with sliced green onions.