Heat oil in a large pot over medium heat. Add in the onions, ginger, and chiles and cook for a few minutes, stirring. Add in the sweet potato, carrots, and cabbage. Cover and cook for about 3 minutes, or until cabbage starts to wilt. Add in the broth and bring to a boil. Reduce the heat to a simmer and cook for 5 minutes.
In the meantime, whisk together the soy sauce, rice vinegar, salt, pepper, cold water, and cornstarch in a separate bowl. Set aside.
Add the zucchini, bell peppers, and tofu to the pot. Simmer until the veggies are tender, about 8 minutes. Add in the soy sauce mixture and stir until the soup thickens, about 8 minutes. Add in the bok choy and tomatoes and bring the soup back to a simmer. Stir in the sesame oil.