On an oiled baking sheet, place squash facedown and cook until tender, about 30-35 minutes. Remove and let cool. Scoop squash flesh into a bowl and set aside, discarding the skin.
Heat oil in a large pot over medium heat. Add sweet potato, onion, garlic, almond milk, broth, curry powder, and cinnamon stick. Cook until sweet potato is tender, about 30 minutes, stirring occasionally. Roughly chop squash and add to pot. Remove cinnamon stick. Using an immersion blender, puree mixture until soup is smooth. Stir in remaining spices and season to taste.
If you do not have an immersion blender, you may put the squash into a blender, then add the soup mixture in batches and puree until smooth.