In a large baking dish bake the banana squash (butternut will work as well), cut sides down, in the middle of a preheated 375° P. oven for 30-45 minutes, or until it is tender when pierced. Discard the seeds and scoop out the flesh with a spoon.
In a kettle cook the onion in the butter over moderately low heat, stirring, until it is softened, add the flour, and cook the roux, stirring, for 3 minutes. Add the broth, the squash, and the vermouth and simmer the mixture, covered, stirring, for 20 minutes.
Purée the soup with a hand blender or in batches in a food processor, return it to the kettle, and add the ginger and the nutmeg. Bring the soup to a boil, simmer it, stirring occasionally, for 10 minutes, and add salt and pepper to taste.