Heat the olive oil in a large pot; add onion and chili powder. Cook until onion is slightly tender, about 4 minutes.
Add the squash, apples, broth and apple cider. If you don’t have apple cider add a little extra broth. You want the liquid at or just below the level of the chopped squash. Bring to a boil, cover and cook over low heat until the squash is very soft, about 30 minutes.
Puree the soup with an immersion blender, adding liquid (water, broth or cider) until it reaches your desired consistency. It should be thick, not watery. You can also transfer soup in batches to a food processor or blender.