04Slice the remaining white onion into very thin slices. Separate the slices, dip the slices into the milk, then into the flour. Fry the breaded onions, a handful at a time in the oil until golden brown. Drain on a paper towel.
05When the soup has simmered for 10 minutes, strain the vegetables out of the broth and toss them out. Pour the broth back into the pan and keep it hot over low heat.
06To serve soup, ladle about 1 cup of broth into a bowl.
07Drop a few pieces of fried onion into the soup, followed by 6 to 8 mushroom slices (about 1 mushroom each) and a couple pinches of diced green onion. When the fried onions sink to the bottom of the bowl (a couple of minutes), serve the soup.