In a large pot over medium-high heat, heat the oil. Add the garlic and ginger and sauté.
Add the onions, celery, and carrots. Cook until the vegetables begin to soften.
Stir in the tofu. Mix well and cook until lightly browned.
Pour in the vegetable broth and milk. Add the beans, thyme, and parsley. Mix until well blended.
Bring the mixture to a boil, then reduce the heat and simmer until the vegetables are tender.
Remove from the heat and add the green onions, salt, and pepper. Mix well.
Purée the soup in a food processor until smooth. Strain through a fine mesh sieve, if desired.