Preheat oven to 375 degrees F. 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, pell (discarding skins). Place flesh in the bowl of a food processor, and process until very smooth. If the puree is very wet, set in a strainer over a bowl and let drain for 1 hour. (Puree can e made ahead and refrigerated in an airtight container up to 3 days.)
On a lightly floured surface, roll out dough to 1/8 inch thick. Transfer to a 9-inch pie dish; trim, leaving 1 1-inch overhang. Fold overhang under and crimp as desired. Refrigerate 15 minutes.
Crumple a large sheet of parchment paper, then use to line pie shell, fill with dried beans or rice. Bake until edges begin to turn golden, 20 to 30 minutes. Carefully remove the beans and parchment; discard. Continue baking the crust until bottom and sides are pal 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.
In a medium bowl, whisk together 1 cup squash puree (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.
Bake 10 minutes. Reduce oven temperature to 325 degrees F 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 pate brisee leaves and sugared cranberries, with whipped cream on the side.
