Heat the oil in a large soup pot over medium heat, and stir in the onion, celery, carrot, garlic, and ginger. Gently sauté just until soft, you don't want any browning. Add a small splash of water if the pan drys out in the process.
Stir in the white pepper and 10 cups of water. Dial up the heat to bring the broth to a simmer, and hold there for about 15 minutes. Add the mushrooms, tofu, and salt, and gently simmer for another 5 minutes. Stir well, taste, and adjust with more salt or water if needed. Ladle the soup into shallow soup bowls and top with lots of green onions, pea shoots, and a few watermelon radish slices. Add a finishing drizzle of olive oil, and enjoy!