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1. Preheat the oven to 425u00b0F. Cover a baking sheet with foil and brush lightly with olive oil. Cut the squash in half, scoop out the seeds and stringy membranes, brush the cut sides with olive oil and lay cut side down on the foil-covered baking sheet. Bake 40 minutes, or until soft enough to pierce easily with a knife. Remove from the heat and allow to cool, then peel and either mash with a fork, puree in a food processor fitted with the steel blade, or finely dice. You should have about 2 cups of pureed or finely diced squash.
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2. Turn the oven down to 375u00b0F and oil a 2-quart gratin or baking dish with olive oil. Heat the remaining oil over medium heat in a medium heavy skillet and add the onion. Cook, stirring, until tender, about 5 minutes. Add the garlic and cook, stirring, until fragrant, 30 seconds to a minute. Stir in the parsley and sage, and squash, and remove from the heat. Season to taste with salt and pepper.
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4. Beat the eggs in a large bowl and whisk in the milk. Add 1/2 teaspoon salt and freshly ground pepper to taste. Stir in the squash mixture and the Gruyere. Taste and adjust seasonings. Scrape into the prepared baking dish and sprinkle the Parmesan over the top.
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5. Bake 30 to 40 minutes, until lightly browned on the top and sizzling. Serve hot, warm, or room temperature.
