Preheat the oven to 350°. Place the squash, cut side down, on a lightly oiled baking sheet. Bake for about 1 hour, until very tender. Let cool slightly, then scoop out the flesh.
In a food processor, combine 3 cups of the squash with 5 tablespoons of the superfine sugar and the maple syrup; puree until smooth. In a small bowl, stir together the ground spices; add them to the squash puree and pulse to blend.
In a small microwave-safe bowl, sprinkle the gelatin over the cold water and let stand until softened, 2 to 3 minutes. Melt the gelatin in a microwave oven at high power, about 10 seconds. Add the gelatin to the squash puree and pulse to combine. Scrape the puree into a large bowl.
In a medium bowl, using a handheld electric mixer, beat the egg whites at medium speed until soft peaks form. With the mixer on, add the remaining 3 tablespoons of superfine sugar and beat until the whites are stiff and glossy. Fold the egg whites into the squash. Pour the heavy cream into the bowl the whites were in and beat at medium speed until firm. Fold the whipped cream into the mousse. Spoon the mousse into 10 parfait glasses and refrigerate until firm, at least 4 hours.
In a small saucepan, combine the sugar, water, vanilla bean and seeds and the pepper and bring to a boil, stirring until the sugar is dissolved. Add the squash and simmer over moderate heat until tender and glossy, about 15 minutes. Let the squash cool in the syrup.
Just before serving, drain the squash. Garnish each mousse with whipped cream and the candied squash and serve with Spiced Almond Tuiles.
The squash mousse and candied squash can be refrigerated for up to 2 days.
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