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Preheat oven to 400 degrees F.
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Butter a large 2-quart baking dish.
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Mix eggs, milk, cream and nutmeg in a medium bowl to combine. Season with salt and pepper.
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Cut baguette into 1-inch cubes. Add bread cubes to the milk/cream mixture stirring well to combine. Let the mixture sit for about 15 minutes to give the bread cubes an opportunity to absorb the custard mixture.
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Cut off an inch or so on each end of the squash and then cut the squash in half. Remove the seeds and strings from the inside of the squash and brush the squash generously with olive oil. Salt and pepper the squash and bake in a 400 degree F. oven until it is tender. This takes about 20 minutes. Test the squash for doneness and, when done, remove from the oven and cool. When the squash is cool, peel it and cut it into 1-inch cubes.
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Wash leek in cold water and trim off the tough green stem. You will only be working with the light green and white parts of the leek. Cut the leek into thin slices and soak in a bowl of cold water to remove any residual sand. Lift leeks out of water, drain and pat dry.
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Wash spinach, drain and pat dry.
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Melt butter in a large pan and sauté the leeks until they are tender (about 5 minutes). Add the spinach to the leeks and cook only until the spinach begins to wilt. Add this leek-spinach mixture to the bowl of bread cubes. Add the roasted squash, gruyere cheese and 1/4 C. grated parmesan. Mix well with your hands.
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Pour the pudding into the prepared baking dish and top with the remaining 1/4 C. parmesan cheese. Bake in 400 degree F. oven for approximately 40 minutes. The pudding will be set and the bread cubes will have golden brown edges when the pudding is done.
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Remove from oven and set on your counter for a few minutes. Serve hot.