Combine the water and 1/4 cup salt in a small saucepan and heat until mixture boils and salt has dissolved; set aside to cool slightly.

Meanwhile, peel ginger; slice thinly with a vegetable peeler or mandolin. Toss with the salt water in a non-reactive bowl and set aside for 1 hour.

Remove ginger to a strainer and rinse thoroughly under cool running water; drain well. Combine the rice vinegar and ginger in a small non-reactive saucepan; set aside 30 minutes.

Stir sugar, mirin, remaining 1/2 teaspoon salt, and the dashi, if using, into ginger mixture; bring to a boil. Remove from heat and set aside to cool to room temperature. Once cool, cover and store in the refrigerator. Ginger will keep up to 1 month and will gradually become a pale pink.