In a soup pot on medium heat, cook the onions in the oil, stirring frequently, for 5 minutes. Add the celery and continue to cook, covered, stirring frequently for 5 minutes. Add some water if the vegetables begin to stick.
Add the mushrooms, lower the heat, and cook until the mushrooms begin to release their juices, about 5 minutes. Stir in the bay leaves, ginger, and tomatoes and cook for 5 minutes.
Stir in the tahini butter, add the tofu, and simmer on a heat diffuser or on very low heat for a few minutes more. Add soy sauce or salt to taste; discard the bay leaves and serve.