How to Make It
Preheat oven to 350°F. Brush cut sides of pumpkin halves with oil. Arrange pumpkin halves, cut side down, on a large rimmed baking sheet lined with parchment paper. Bake in preheated oven until very tender when pierced with a fork, about 50 minutes. Remove from oven, and let cool slightly, about 10 minutes.
Scoop flesh from cooled pumpkin; transfer to bowl of a food processor. Discard pumpkin shell. Add apple cider; process until smooth, about 1 minute, stopping to scrape down sides of bowl as needed. Add brown sugar, honey, vinegar, cinnamon, ginger, salt, nutmeg, and cloves; process until smooth, about 20 seconds, stopping to scrape down sides as needed.
Transfer pumpkin mixture to a saucepan; bring to a simmer over medium, stirring occasionally. Reduce heat to low; cook, stirring occasionally with a rubber spatula to ensure bottom of saucepan does not scorch and sides of saucepan stay clean, until mixture is reduced by one-third and turns slightly darker in color, about 25 minutes. Remove from heat; let cool to room temperature, about 30 minutes.