Partially steam the squash halves, cut sides down, on a rack over gently boiling water until tender, about 10 minutes. Cool briefly. Scrape squash pulp from the shells with a spoon and set aside.
Combine the apples, onion, curry powder, and ¼cup of the broth in a medium saucepan. Cook the mixture over low heat, covered, for 10 minutes. Add the squash pulp, the remaining broth, apple juice, ginger, and ½teaspoon salt. Simmer over low heat, covered, for 20 minutes.
Working in batches, puree the soup in a food processor or blender until smooth. Rinse the saucepan and set a sieve over the pan. Press the puree through the sieve. Reheat the soup, add the lemon juice and additional salt and pepper to taste.
Discard the yogurt water and transfer the yogurt from the strainer to a small bowl. Stir in the mint and cilantro, if using. Garnish each serving with a spoonful of yogurt.