Preheat your oven to 350 degrees F. In a small bowl, whisk together the white miso and hot water. Spread the moon-shaped half rings of delicate squash onto a parchment-lined baking sheet. Brush both sides of squash with the miso. Sprinkle with a few pinches of salt. Transfer to the oven to roast for 15 to 20 minutes, until the squash is tender when poked with a fork. Set aside to cool.
To a mortar and pestle, add the garlic cloves, sugar and salt; pound into a paste. Pour in the olive oil and work it into the paste. In a small skillet, set over medium heat, add the sugar paste mixture and mushrooms; toss until the mushrooms and cook for 2 to 3 minutes, until tender. Set aside.
To assemble: Fill a large bowl with warm water. Dip one wrapper into the hot water for 1 second until slightly softened (it’ll become softer as the water sets in so don’t over soak). Lap the wrapper flat on your work surface. In a row across the center, place the slices of squash, top with a few spoonfuls of mushrooms and a small handful of radish sprouts. Fold in the sides inward, then tightly role the wrapper, beginning at the end. Repeat with the remaining ingredients and wrappers. If kept in an airtight container, spring rolls will keep well for 2 to 3 days.