Preheat the oven to 350 degrees F (175 degrees C).
Cut the squash in half, and remove the seeds and any excess membrane. Place cut side up in a baking dish. Cover the dish and bake for 45 minutes.
Meanwhile, combine the cinnamon, pineapple, nutmeg, allspice, and ginger. When squash has been cooked, remove from oven. Let cool down for 10 minutes.
Carefully scoop out the pulp from both halves and combine with the pineapple and cinnamon mixture. Replace mixture into shells and return to the oven and bake for 7 minutes until pineapple is hot and bubbly.