Slice papaya in half and remove seeds. Cut into small chunks.
Place in a steamer basket over water, and steam for about 10 minutes, or until very tender.
Once cool, scrape the papaya from the skin and place into a food processor or blender.
Purée for about 30 seconds. Add leftover cooking water, 1 tablespoon at a time, and continue puréeing until papaya is smooth.
Very ripe papayas can be fork-mashed instead of puréed.