Rinse the roe carefully and gently pat it dry. With a sharp knife, split the roe in two.
In a wide shallow pot (or deep wide skillet), combine the kelp and water over high heat. Remove the kelp when the water begins to bubble, and season the broth with the remaining simmering-liquid ingredients. Over low heat, simmer the liquid for 1-2 minutes, stirring occasionally to dissolve the sugar.
Line your pot or skillet with a dried bamboo leaf or cooking parchment (see the note). Press lining in place with liquid in the pot. Carefully lay the pieces of roe on top.
Simmer the roe for about 4-5 minutes, frequently ladling the gently bubbling liquid over it, until it is no longer pink. The roe will curl and “blossom” as the skin shrinks, exposing the eggs inside. To remove the cooked roe, lift up the sling-like bamboo leaf or parchment. Carefully transfer each piece to an individual serving plate.
Peel the knob of ginger, then slice it into tissue-thin slices. Stack these on each other and cut them into thread-like slivers. Soak these in a bowl of ice water for 1-2 minutes.
Combine the cornstarch and cold water in a small cup to make a paste. Thicken the remaining simmering liquid with the cornstarch paste, and spoon this sauce over each portion of roe. Drain the ginger threads, garnish each serving of roe with a portion of slivered ginger.