Prepare the Squash: Cut the butternut squash into 12 strips, each about 4 x ½ inches (10 x 1. 25 cm).
In a small pot, combine the Vegetarian Dashi, garlic, and fresh ginger.
Bring to a rapid boil over high heat.
Simmer the Squash: Reduce the heat to a simmer and stir in the soy sauce.
Place the squash strips in a wire basket or strainer and lower them into the simmering liquid.
Cook until the squash is tender but not mushy, about 5–7 minutes. Carefully remove the squash from the liquid and set aside to cool completely.
Prepare the Nori & Rice: Place one nori sheet horizontally on a bamboo rolling mat, with the rough side facing up.
Dip your fingertips in water to prevent sticking, then spread about ½ cup (100 g / 3.5 oz) of the prepared sushi rice in a thin, even layer across the bottom three-quarters of the nori sheet.
Add the Fillings: Arrange 2 of the cooled butternut squash sticks horizontally across the center of the rice.
Sprinkle ½ teaspoon of the finely chopped crystallized ginger over the squash, followed by a portion of the sliced green onions.
Roll the Sushi: With your thumbs under the bamboo mat, use your fingers to hold the fillings in place and fold the bottom edge of the mat up and over, tucking the edge of the nori just past the fillings to start the roll. Be careful not to roll the mat itself into the sushi.
Shape and Seal: Lift the edge of the mat and continue to roll forward, applying gentle, even pressure.
Once rolled, gently shape the roll into a soft rectangle by pressing with your forefingers on top and your thumbs and middle fingers on the sides.
Let the completed roll rest seam-side down on a cutting board.
Repeat and Serve: Repeat the process to make the remaining 5 rolls.
Using a very sharp knife dipped lightly in water, slice each roll into 6 even pieces.
Serve immediately with Vegetarian Eel Sauce for dipping, if desired.
Keep a small bowl of water handy to wet your fingertips when handling sushi rice. This prevents it from sticking to your hands.
Don't overcook the squash. You want it tender enough to bite through easily but firm enough to hold its shape in the roll.