In a heavy soup pot, heat oil over medium heat. Add onions and garlic; sauté for 2 to 3 minutes, or until slightly softened. Stir in curry and cumin and cook for 1 minute. Add chicken stock, cider, rice and squash; bring to a boil. Reduce heat to low and cover the pan; simmer for 30 to 40 minutes, or until the squash is tender.
Pour the mixture through a strainer set over a large bowl. Puree the solids in a food processor or blender until very smooth. Return the puree and liquid to the saucepan. (The soup can be prepared ahead and stored, covered, in the refrigerator for up to 2 days.)
To serve, heat the soup gently and season with salt and pepper. In a small bowl, stir together yogurt and milk. Ladle the soup into bowls, and add a dollop of the yogurt mixture. Draw the tip of a knife or a toothpick through the yogurt to make decorative swirls.