1. Set a large pot of salted water to boil on high.
2. Pat the chicken dry with paper towels; season with salt and pepper on both sides.
3. In a medium pan, heat a drizzle of olive oil on medium-high. Add the seasoned chicken and cook 5 to 7 minutes per side, or until browned and cooked through. Leaving any browned bits (or fond) in the pan, transfer the cooked chicken to a cutting board. When cool enough to handle, using 2 forks, carefully shred into bite-sized pieces.
4. While the chicken cooks, wash and dry the fresh produce. Halve the tomatoes; place in a medium bowl and season with salt and pepper. Thinly slice the cucumber into rounds. Cut off and discard the root ends of the scallions; thinly slice, separating the white bottoms and green tops. In a bowl, whisk together the miso paste, water, sesame oil, and half the mirin.
5. Add the cucumber, half the ginger, and the remaining mirin to the bowl of seasoned tomatoes. Stir to thoroughly combine. Set aside to marinate, stirring occasionally, for at least 10 minutes. Season with salt and pepper to taste.
6. While the vegetables marinate, add the corn, white bottoms of the scallions, and remaining ginger to the pan of reserved fond; season with salt and pepper. Cook on medium-high, stirring occasionally, 2 to 3 minutes, or until slightly softened and fragrant. Turn off the heat.
7. While the corn cooks, add the noodles to the pot of boiling water, stirring gently to separate. Cook, stirring occasionally, 3 to 10 minutes, or until tender. Turn off the heat. Drain thoroughly and rinse under cold water to prevent sticking. Return to the pot. Add the tamari and all but a pinch of the kombu; gently toss to combine.
8. In a large bowl, combine the shredded chicken and sauce. Stir to coat; season with salt and pepper to taste.
9. Top the dishes of dressed noodles with the finished chicken (including any sauce from the bowl), cooked corn, and marinated vegetables (including any marinating liquid). Garnish with the green tops of the scallions. Garnish the marinated vegetables with the remaining kombu.