1 Preheat the oven to 400° F.
2 Halve the squash lengthwise with a sharp knife and scoop out the seeds and fibers. Place cut side up in a shallow baking dish and cover tightly with foil. Or, if you’d like a more roasted flavor, simply brush the squash halves with a little olive oil and leave uncovered. Either way, bake for 45 to 50 minutes, or until tender. Set aside until cool enough to handle.
3 Heat the oil in a soup pot. Add the onion and sauté over medium-low heat until golden, 8 to 10 minutes.
4 Add the apples, broth, and spices. Bring to a simmer, then cover and simmer gently until the apples are soft, about 10 minutes.
5 In a food processor, puree the squash with ½ cup of the milk until completely smooth. Transfer to a bowl.
6 Transfer the apple-onion mixture to the food processor and purée until completely smooth. Return to the soup pot and add the squash purée; stir together. Add the remaining milk, using a bit more if the purée is too thick.
7 Bring the soup to a gentle simmer, then cook over low heat until well heated through, 5 to 10 minutes. Season with salt and pepper. Serve at once, or let the soup stand off the heat for 1 to 2 hours, then heat through as needed before serving.