Step 1

In a large (5-quart) pot, combine broth, soy sauce, crushed red pepper, and 2 cups water. Bring to a boil over medium heat. Add mushrooms; reduce heat, and simmer until tender, about 10 minutes.

Step 2

In a small bowl, whisk together 3 tablespoons vinegar and cornstarch. Add to pot; simmer, stirring, until soup is thickened, about 1 minute.

Step 3

Add egg through a slotted spoon, and stir to form ribbons. Stir in tofu. Remove from heat; let stand, covered, 1 minute. Put ginger in a small sieve, and squeeze to release juice into soup (discard solids). Taste; add remaining tablespoon vinegar, if desired. Serve sprinkled with scallions.