Soak the dried kombu and shiitake mushrooms overnight in room-temperature water for the best flavor. If you are short on time, soak them for at least 10 minutes in boiling water with a lid to retain the steam. Do not discard the liquid.

Bring a medium-sized pot of water to a boil over medium-high heat. Add the noodles and cook for 1 to 2 minutes less than the package instructions so they remain very chewy and have a bite. Drain immediately and run under cold water to remove excess starch, then divide the noodles into two bowls.

Add the kombu, mushrooms, and soaking liquid to the same pot. Cover and bring to a boil over medium-high heat. Stir in the sake, mirin, soy sauce, and salt, then simmer for 6 to 7 minutes to develop the broth.

Place the dried wakame in a small bowl and pour boiling water over it. Let it rehydrate for 2 to 3 minutes until it has quadrupled in size, then drain well.

Remove the kombu and mushrooms from the broth. Slice them into thin strips to include as a topping if you prefer.

Place the wakame, mushrooms, and kombu over the noodles. Pour the hot broth into the bowls and finish with a sprinkle of seven-spice blend and scallions. Serve immediately while the broth is steaming and the noodles are still firm.