Preheat the oven to 400° F. Line a baking sheet with aluminum foil and oil the foil. Cut the squash in half lengthwise and scrape out and discard the seeds. Place the squash halves, cut side down, on the prepared baking sheet. Bake until tender throughout, about 40 minutes. Test for doneness with a sharp knife or thin skewer; it should meet no resistance. Remove from the oven and, when cool enough to handle, peel off the skin and cut the squash into small dice.

In a soup pot, melt the butter with the olive oil over medium-low heat. Add the onions and sautè very gently until thoroughly softened but not at all browned, 10 to 12 minutes. Add the diced squash and the ginger and sautè to marry the flavors, about 5 minutes. Now stir in 3 cups of the milk and cook over low heat until the mixture begins to simmer. Remove the pot from the heat and allow the mixture to cool somewhat. Then pass the mixture through a food mill or purèe in a blender or food processor. Return the purèe to the pot, stir in the remaining 5 cups milk, and simmer for about 12 more minutes to thicken. Add more milk if the consistency is too thick (it should be thick enough to coat the spoon) and heat through. Season with the salt and pepper.

Ladle into warmed bowls, strew the mint on the surface, if using, and serve at once.