In a large saucepan or stockpot, combine the celery, onion, carrot, ginger, garlic and a few of the mushrooms. Add beef stock. Bring to a rolling boil over high heat. Cover, reduce heat to medium, and simmer for 45 minutes.
Place all of the remaining mushrooms into a separate saucepan. When the vegetable-beef stock is ready, place a sieve over the pan with the mushrooms in it. Strain the vegetable-beef stock into the pan. Discard strained vegetables.
Serve the mushroom soup in small porcelain bowls, and sprinkle fresh chives over the top.