In a large pot, heat the sesame oil over medium heat. Add the ground pork and cook until browned, breaking it apart with a spoon, about 5-7 minutes.
Add the shredded carrots, chopped cabbage, sliced mushrooms, garlic, and ginger to the pot. Sauté for another 5 minutes until the vegetables are softened.
Pour in the chicken broth, coconut aminos, rice vinegar, salt, and black pepper. Stir well to combine.
Bring the soup to a boil, then reduce the heat and let it simmer for 10-15 minutes, allowing the flavors to meld.
Taste and adjust seasoning if necessary. Serve hot, garnished with sliced green onions and sesame seeds if desired.