In a kettle or large saucepan, quickly sauté ginger slices in peanut oil for several minutes. Remove and discard the ginger.
Add the sesame oil, sesame seeds, carrots and scallion whites (save the greens for later). Salt the mixture lightly, and grind in some fresh black pepper. Sauté over medium heat for 5 minutes, stirring frequently.
Add the tamari, stock or water and chopped tomatoes. Cover, and let it cook over medium heat about 10 minutes more.
At this point, the soup is ready to rest until just before serving time. About 10 minutes before serving time, add the vinegar, peas and optional black mushrooms.
Heat the soup to a gentle boil. Stir the soup in a circular direction with a long chopstick, and drizzle in the beaten egg in a thin, steady stream.
Continue stirring the simmering soup for about 5 more minutes.
Serve topped with minced scallion greens.
From The Enchanted Broccoli Forest, Mollie Katzen.