Bring the ginger and wine to a simmer in a small pot. Remove from heat and steep while you prepare the soup.
In a large pot, cook the onions, celery, and garlic in 1/2 cup of the broth until the onion is wilted.
Add the rest of the chicken broth and squash and bring to a simmer. Continue to simmer until the squash is tender. If necessary, add more broth or water.
Using a food processor or blender, puree squash mixture until smooth. If using a food processor, do this in batches so the machine does not overflow.
Whisk in the yogurt and milk. Discarding the ginger, drain the wine and pour it into the soup. Reheat (do not allow to boil to avoid curdling) and serve with a dollop of yogurt and a sprinkling of chives.