Preheat the oven to 400 degrees F (200 degrees C). Cover a baking pan with aluminum foil and coat with vegetable oil.
Remove acorn squash stems, cut in half lengthwise, and clean out the seeds. Place squash cut side-down onto the prepared baking pan.
Roast in the preheated oven until tender, 30 to 60 minutes, depending on the size of the squash
While squash roasts, place brown sugar, butter, sea salt, cinnamon, and allspice in a small bowl. Microwave to melt the butter, about 30 seconds; stir to combine.
Remove squash from the oven, turn over, and coat with the sugar mixture. Continue to roast for 5 minutes more.