Bring water, tamari, mirin, kombu, sesame oil, and dashi to a boil in a large pot. Add soba noodles; cook, stirring occasionally until soft and tender, about 5 minutes. Mix in spinach, lemon cucumber slices, bean sprouts, and scallions. Cook until vegetables have softened, about 3 minutes.
Remove from heat. Discard kombu strips. Sprinkle with cilantro; serve.