Prepare the vegetables. Cut tomatoes into wedges and mushrooms into slices. For the leafy greens with large stalks such as bok choy, you may separate the leave and stalk so they cook quickly.
Make the dough. In a large mixing bowl, whisk together the dry ingredients until well-combined. Fill a one-hole bottle with ¼ cup of water. Squeeze the water in batches into the flour and start shaking while moving the bowl in a circular motion (think of hula hoop) until lumps of flour form. You may not need all the water.
Make the soup. In a heated pot with 1 tablespoon oil, sauté ginger and mushrooms until fragrant. Continue to sauté the green onion tops.
Add the tomatoes and cook until they release their juices. Season with soy sauce and stir in the green onion tops. Once you add the vegetable stock, add a dash of white pepper and bring it to a boil.
Then, drop in the dough in a sprinkling mode all over the soup so the dough doesn't clump together in one place. Note: It's important that the soup is boiling when you add the dough. Let this mixture cook for another minute, then use a spatula to stir to combine.
Finally, add the vegetables and cook until they are as crisp as you like. Taste and season accordingly.
Swirl in a splash of toasted sesame oil or chile oil, and garnish with chopped green onions. Serve warm.