Kabocha and Red Kuri. Word has it that all squash originated in Mesoamerica. When the kabocha was introduced to Japan in the sixteenth century by Portuguese sailors, it was quickly adopted as a cherished component of Japanese cuisine. The story of the Red Kuri’s journey to Japan has been lost, but it’s become equally popular. The sweet, nutty flavor of the flesh of both varieties is often compared to chestnuts.