Cut off the hard part from the top and bottom of the squash; cut into 4 wedges. Scoop out seeds with a spoon and cut into chunks.

Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil over medium-high heat. Add squash, cover, and steam until tender and a chopstick is easily pushed through the center, 12 to 15 minutes. Remove and leave covered for about 5 minutes.

Remove skin from the squash and mash flesh by using a food processor or by pushing it though a sieve with a wooden spoon into a bowl.

Transfer mashed squash to a mixing bowl. Add flour, egg yolks, water, cornstarch, sugar, salt, and cinnamon. Mix well.

Roll out a sushi, or makisu, mat as if you were making a sushi roll. Wet a dish towel or muslin cloth slightly with water and lay on the mat. Spread squash mixture evenly on top. Hold the nearest end and tightly roll up the mat to the other end. Close both outer ends by rolling up or folding the towel.

Place the rolled squash mixture in the mat back into a steamer insert in a saucepan; steam for 5 minutes. Remove from heat and let sit for 5 minutes. Open the sushi mat and cut the cake into 1-inch thick slices. Serve cold on 4 small plates with Asian pears and/or persimmons.