In a medium bowl, whisk together the flour, allspice, cinnamon, ginger, nutmeg, baking powder, and salt; reserve. In a large bowl, using an electric mixer set on medium-high speed, beat together the butter, brown sugar, and granulated sugar until light and fluffy. Add the egg yolk and vanilla and beat well. Beat in the pumpkin puree. Reduce the speed to low and add the flour mixture in 3 batches, mixing well after each addition. Turn out the dough onto a lightly floured surface, divide in half, flatten each half into a disk, wrap separately in plastic wrap, and chill for 30 minutes. Preheat an oven to 350 degrees F. Line 2 baking sheets with parchment paper. On a lightly floured surface, roll out 1 of the disks 1/8-inch thick. Using a pumpkin-shaped cookie cutter or cardboard Jack-o'-lantern template 5 to 6 inches in diameter, cut out cookies. If using the cookie cutter, finish off the Jack-o'-lantern by cutting out eyes and a mouth with the tip of a sharp knife. Repeat with the remaining dough. Transfer the cookies to the prepared baking sheets. Bake until golden, 12 to 15 minutes. Transfer to a wire rack to cool. Decorate with colored sugars/chocolates.
Preheat an oven to 400 degrees. Brush a baking sheet with the oil.
Cut the pumpkin in half horizontally and scoop out the seeds and strings (save the seeds for roasting). Place the pumpkin halves cut side down on the prepared baking sheet. Bake until the flesh is soft when pierced with a fork, 45 to 60 minutes. Remove from the oven and let cool.
Scoop out the flesh into a food processor or blender. Puree until smooth. Spoon the pumpkin puree into a sieve placed over a large bowl. Let the pumpkin drain for 30 minutes before using. Cover and refrigerate for up to 1 week, or freeze up to 1 year.