Pumpkin Pie of the World
England baked pumpkin in a lidded pie with apples and spice in the 1600s. New England turned it into a smooth custard in an open crust, the South made it with sweet potatoes, and a can made it a Thanksgiving rule. Elsewhere, pumpkin is candied in dark syrup in Mexico, baked in its own juice in Turkey and steamed into custard in Japan and Thailand.

Pumpion Pie (Hannah Woolley's 17th-Century English Pumpkin Pie)
Before the custard there was this: slices of squash browned in butter and baked under a pastry lid with tart apples, raisins, currants, sugar, spice and a splash of sherry, adapted from a 1670s English recipe.

Calabaza en Tacha (Mexican Candied Pumpkin in Piloncillo)
Wedges of whole pumpkin, skin and all, simmered for two hours in a dark syrup of piloncillo, cinnamon and orange until they turn deep brown and glossy, the candied pumpkin of Mexico's Day of the Dead.

Doce de AbΓ³bora em Calda (Brazilian Pumpkin Cubes in Syrup)
Neat cubes of pumpkin soaked briefly in limewater, then simmered for two hours in a light sugar syrup and left to steep overnight, so they turn glassy and sweet while staying firm, the Brazilian way.

Kabak TatlΔ±sΔ± (Turkish Candied Pumpkin with Tahini and Walnuts)
Thick blocks of pumpkin layered with sugar and left overnight to make their own syrup, then baked until candied and served cool with crushed walnuts and a drizzle of tahini, no water added.

Kabocha Purin (Japanese Kabocha Pudding with Caramel)
Japan's custard pudding made with sieved kabocha squash, baked in a water bath over dark caramel, chilled and turned out so the caramel runs down the sides.

Sangkhaya Fak Thong (Thai Coconut Custard Steamed in a Whole Squash)
A small kabocha hollowed out, filled with coconut cream, palm sugar and egg custard scented with pandan, steamed until set, chilled and cut into wedges that show a yellow custard heart in an orange shell.

Classic American Pumpkin Pie
The Thanksgiving pie: a smooth custard of pumpkin puree, eggs, heavy cream, sugar, cinnamon, ginger and nutmeg in a par-baked all-butter crust, pulled from the oven while the center still wobbles.

New England Squash Pie (Lydia Maria Child, 1832)
The old Yankee custard pie made with roasted winter squash instead of pumpkin, cooked with milk, sweetened with molasses and a little sugar, spiced with plenty of cinnamon and ginger, and baked in an open crust.

Southern Sweet Potato Pie
Silky sweet potato custard made with brown sugar, butter, sour cream, extra yolks, cinnamon, nutmeg and an optional splash of bourbon, baked in a crust lined with a thin layer of caramelized brown sugar.

Pumpkin Chiffon Pie
All the spice of pumpkin pie in a light, mousse-like filling: a cooked pumpkin custard set with gelatin and folded with whipped cream, piled into a toasted walnut and graham cracker crust and chilled, no baking of the filling.

Pumpkin Bread (Chocolate Chip Quick Bread)
King Arthur's super-moist oil-based pumpkin quick bread, made with canned pumpkin, nutmeg and vanilla, studded with chocolate chips and baked in one loaf pan.
Crustless Pumpkin Pie Cups
Classic pumpkin pie filling baked without the crust in six ramekins in a water bath, so it is in the oven in 10 minutes and ready in about 45, with the silky texture of the pie and none of the rolling.
Spiced Pumpkin Loaf with Pepitas, Inspired by Starbucks
A tender, heavily spiced pumpkin loaf sweetened with sugar and honey, scented with cinnamon, nutmeg, cloves and ginger and topped with crunchy pepitas, in the style of the coffee-shop pumpkin loaf. Inspired by, not official.