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Preheat oven to 425°F.
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Wash butternut squash. With large chef’s knife, slice the squash in half, vertically. With large spoon, scoop out the seeds and fibrous matter from the interior of each squash half (save the seeds for roasting!)
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Prepare large rimmed baking sheet by lining with tin foil sprayed lightly with cooking oil. Lightly brush the cut sides and scooped out hollow of the squash halves with olive oil. Sprinkle with salt and pepper. Place the squash halves, cut side down, on the baking sheet. Roast the squash in preheated oven for about 35 minutes. Remove the squash from the oven and, with a large flat lifter, carefully flip the squash pieces over, applying another light brushing of olive oil to the flesh side. Return the squash to the oven for about another 15-20 minutes, or until the flesh of the squash is very soft when pierced with a fork. Remove from oven and let squash cool for 10 minutes or so. Scoop out the flesh and place in medium-sized bowl. (Do not let squash cool completely as it will be difficult to remove from its skin.)
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In large stockpot, heat the butter over medium heat till melted. Add the olive oil. Add the onion, celery, carrot, and parsnip. Stir briskly for 4-5 minutes. Add the garlic and cook for another minute, continuing to stir the mixture.
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Add the chicken stock, apple, and spices. Bring to a boil over medium high heat then reduce heat to medium-low and cook until vegetables are soft, about 10-15 minutes. Remove from heat and cool for about 30 minutes. Remove and discard bay leaves. Stir in cooked squash.
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Purée soup mixture in blender until very smooth. Work in batches, starting with one cup of the mixture, puréeing it until smooth, then adding another 1 to 1½ cups, never filling the blender jug more than a scant half full at a time. Transfer puréed mixture to clean stockpot. Add the maple syrup and milk. Stir well. Heat slowly over medium-low heat but do not boil. Add the Parmesan and cheddar cheese. Stir until cheeses are melted. Serve plain or garnish with croutons and some toasted squash seeds, a dollop of sour cream with a sprinkle of fresh herbs, or a toasted baguette slice topped with cheese, herbs, and bacon.