Heat oven to 400°F. Line rimmed baking sheet with foil; oil foil.
Cut butternut squash lengthwise in half and scoop out and discard seeds. Working on prepared baking sheet, coat squash with 2 tablespoons oil and season with 3/4 teaspoon salt and 1/4 teaspoon pepper. Turn squash cut sides down and roast in lower half of oven until flesh is beginning to turn golden brown, 30 to 35 minutes.
Meanwhile, toss shallots and thyme with remaining tablespoon oil and 1/4 teaspoon each salt and pepper. Turn squash, scatter shallots and thyme on top, then drizzle with maple syrup. Roast until skin is golden brown and crisp, 40 to 50 minutes more.
Let sit until cool enough to handle. Working in batches, scoop some of the softened squash and shallots from the peels into a food processor and puree until smooth.
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