In a small mixing bowl, combine the chilled kombu dashi, soy sauce, mirin, and brown sugar.
Whisk until the sugar is completely dissolved.
Set the soup base aside in the refrigerator to stay cold.
Place the dried wakame in a bowl and cover with cold water.
Let it soak for 5-10 minutes, or until it has softened and expanded.
Drain thoroughly.
Slice the peeled and seeded cucumbers lengthwise as thinly as possible to create long, noodle-like strands. For the best texture, you can toss the cucumber slices with a pinch of salt, let them drain in a colander for 15 minutes, then rinse and gently squeeze dry.
To serve, divide the rehydrated wakame among four individual serving bowls. Artfully arrange the cucumber 'noodles' on top of the seaweed, twisting them into little nests if you like.
Just before serving, drizzle each portion with a tablespoon of toasted sesame oil.
Garnish generously with sliced scallions, toasted sesame seeds, and a sprinkle of Japanese Seven-Spice Mix.
Pour the chilled soup base over the at the table for a beautiful presentation.
Don't over-soak the wakame! It only needs about 5-10 minutes in cold water to rehydrate. It should be tender but still have a slight, pleasant chew.