STEP 1

Preheat oven to 375°. Place squash cut-side down on a parchment-lined rimmed baking sheet. Roast until almost completely tender when pierced with the tip of a knife, 45 minutes to 1 hour. Turn cut-side up and roast until very tender and beginning to dry out a bit on top (but not brown). When cool enough to handle, peel (discarding skins). Place flesh in the bowl of a food processor, and process until very smooth. If the purée is very wet, set in a strainer over a bowl and let drain for 1 hour. (Purée can be made ahead and refrigerated in an airtight container up to 3 days.)

STEP 2

On a lightly floured surface, roll out dough 1/8 inch thick. Transfer to a 9-inch pie dish; trim, leaving a 1-inch overhang. Fold overhang under and crimp as desired. Refrigerate 15 minutes.

STEP 3

Crumple a large sheet of parchment paper, then use to line shell, fill with dried beans or rice. Bake until edges begin to turn golden, 20 to 30 minutes. Carefully remove beans and parchment; continue baking until bottom and sides are pale brown, about 10 minutes more. Let cool completely on a wire rack. (Crust can be stored at room temperature, covered tightly in foil, overnight.) Transfer to a parchment-lined baking sheet.

STEP 4

In a medium bowl, whisk together 1 cup squash purée (reserve any remainder for another use), cinnamon, allspice, and salt until well combined. Whisk in eggs, maple syrup, milk, and heavy cream. Pour into crust filling to just below rim.

STEP 5

Bake 10 minutes. Reduce oven temperature to 325° and bake until filling is just set in center, 40 to 55 minutes more. Transfer to wire rack; let cool completely. Refrigerate, uncovered, at least 4 hours or, covered, up to 2 days. Serve, topped with piecrust leaves and candied cranberries, with whipped cream on the side.