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Preheat oven to 400 degrees. Prepare your baking trays by setting a wire cooling rack over each (so the wings may cook on all sides).
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Place about 12 wings per tray, skin-side down. Bake in oven for 15 minutes.
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Meanwhile, combine all remaining ingredients in a medium pot, let come to a boil, cover and cook until the squash is soft, about 5 minutes. Remove from heat and place contents in a food processor, chopping until a smooth paste has formed. Move paste to a large bowl.
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Take chicken wings out of the oven and toss in the squash mixture, then gently place back on their wire trays, skin side up for another 15 minutes, a total of 30 minutes cooking time.