Place the rice in a medium bowl and cover it with cool water. Let the rice soak for 15 minutes. (Some rice hulls may float to the top. I like to keep them as the darker flecks give the finished rice character.) Drain the rice in a fine mesh strainer.
Place the rice and measured water in a rice cooker. Cook for exactly 50 minutes. At some point before, the rice cooker may indicate that the rice is done. Do not lift the lid or stop the cooking process before 50 minutes.
While the rice cooks, prepare the dressing. Stir together the rice vinegar, honey or sorghum, sugar, and salt in a small non-metal bowl. Whisk it vigorously until most of the sugar and salt dissolve, about 2 minutes. Set the mixture aside.
Spoon the steamed rice onto a flat cutting board. It should seem a bit moist and starchy. Spread the rice into a thin layer across the cutting board. Drizzle ? cup (80 ml) of the dressing over the rice. Gently toss it. Add the remaining ? (80 ml) of the dressing and toss well.
Allow to cool, uncovered for 10 minutes. Flip the rice over and let it cool for 5 minutes. Place the rice in a large non-metal bowl and cover with a damp, lint-free dishcloth until ready for use. Use it within 4 hours.
Make the Butternut Squash Rolls
Cut the butternut into 12 strips about 4 x ½ inch (10 x 1.25 cm) and set aside. Combine the Vegetarian dashi, garlic, and fresh ginger root in a small pot. Bring to a rapid boil over high heat. Reduce to a simmer and add soy sauce. Place the squash onto a wire basket or strainer and lower into the simmering liquid. Allow the squash to simmer until soft, but not too mushy, 5-7 minutes. Lift the basket from the simmering liquid and allow pieces to cool completely.
Place 1 sheet of the nori rough side facing upwards horizontally on a bamboo rolling mat. Wet your fingertips in water then spread about ½ cup (100 g) of prepared Sushi Rice in a thin, even layer across the bottom ¾ of the nori.
Arrange 2 of the butternut squash sticks horizontally in the center of the rice. It is okay if the ends overlap some in the center. Sprinkle ½ teaspoon crystallized ginger over the top. Add some of the green onions.
Dip your fingertips in water again. Place your thumbs underneath the bamboo rolling mat. Fold the bottom of the mat so that the bottom edge of the nori fits just over the butternut. (Do not allow the edge of the mat to get stuck in the fold!)
Lift the edge of the mat. (The nori should stay in place.) Continue rolling until the roll is complete. Gently shape the roll into a rectangle by pressing your forefingers on top of the mat while simultaneously pressing your thumbs and middle fingers into the sides.
Allow the rolls to rest seam side down on a cutting board. Meanwhile, repeat the steps to complete the remaining rolls. Cut each roll into 6 pieces using a very sharp knife dipped lightly in water. Serve immediately.