Cut the acorn squash in half and remove the seeds. Place the squash into a baking dish, cut side down. Add enough water to cover the bottom 1/2 inch of the pan.
Cook the squash in a 350°F oven for about 45 minutes, or until tender when poked with a fork. When the squash is cool enough to handle, remove and discard the skins.
In a medium-sized pot, sauté the onions in butter over medium heat until they become translucent.
Add allspice, cardamom, white pepper, and salt, and stir until the spices become fragrant. Add chicken broth and cooked squash, and cook until heated through.
Use either a stick blender or a regular blender to puree the soup until smooth. Return the soup to the pot, and add the heavy cream. Heat through, and avoid boiling after the cream has been added.