Bring a large saucepan of water to a boil. Break the soba noodles in half and cook according to package directions until al dente. Drain, then rinse briefly under cool water and set aside.

Meanwhile, combine the vegetable broth, sliced shiitake mushrooms, soy sauce, rice vinegar, sugar, and ginger in a soup pot over medium-high heat. Bring to a rapid simmer, then lower the heat, cover, and simmer gently for 10 minutes.

Stir in the scallions, tofu, spinach, and bok choy (if using). Cover and cook over medium-low heat until the spinach is wilted but still bright green, about 3 minutes.

Stir in the cooked noodles and add the 2 cups of water, or enough to give the soup a dense but not overly crowded consistency. Season with pepper and a little more soy sauce if needed. Heat through for a minute or two and serve at once.