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Position a rack in the center of the oven and preheat to 375ºF. Rub the cut edges of the kabocha squash pieces with the oil, leaving the seeds in for now (they’re easier to remove after roasting), and place cut side down on a rimmed baking sheet. Roast until very tender and slightly collapsing, 35 to 45 minutes. Let cool, scoop out and discard the seeds and strings, and scoop out and reserve the flesh, discarding the skin. Puree the flesh in a food processor until smooth.
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Decrease the oven temperature to 325ºF. Make the filling: In a medium bowl, whisk together the sugar, cinnamon, ginger, nutmeg, allspice, and salt. Whisk in the eggs, then the maple syrup, 1-1/4 cups of the kabocha puree, and the sour cream, milk, and vanilla. If you want the filling super-smooth, strain it through a medium-mesh sieve.
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Pour the filling into the parbaked crust and bake at 325ºF until the tart wobbles slightly like Jell-O when jiggled, 30 to 40 minutes. Cool for 1 hour, then refrigerate until firm, about 2 hours.
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Make the topping: Whip the cream, sour cream, maple syrup, and vanilla to firm peaks. Spread over the tart, top with the hazelnuts and a drizzle of maple syrup, and serve.