Pour the chicken broth in a medium sized pot (make sure it has a lid that fits on the pot).
Add sliced ginger, green onions, shaoxing wine, salt, pepper and sesame oil.
Place a lid on the pot and turn the heat to medium high for 10 minutes.
Remove lid: discard the ginger and green onions.
Turn the heat up to high and bring the broth to a boil.
Add 10-15 wontons to the pot. Cook for 4 minutes or until they float. Remove the wontons with a slotted spoon and transfer to a serving bowl. Depending on the size of your pot, you may need to do this in batches.
Season the broth with salt and pepper.
Place the chopped green onions on top of the cooked wontons. Pour hot broth over cooked wontons.