In a large baking dish bake the squash, cut sides down, with enough water to reach 1 inch up the sides of the dish, covered, in the middle of a preheated 375 degrees F oven for 45 minutes, or until it is tender when pierced. Discard the seeds and scoop out the flesh with a spoon, reserving 3 cups flesh.
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 reserved squash, and the vermouth and simmer the mixture, covered, stirring, for 20 minutes.
Puree the soup in batches in a blender, 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. In a small bowl beat together the yolks and the half-and-half, add 1 cup of the soup to the yolk mixture, whisking, and whisk the yolk mixture into the remaining soup.