Bring a medium pot of water to a boil. Add the soba noodles and cook until just tender, 4 to 5 minutes. Drain and rinse under cold water.
While the soba cooks, start the chicken.

• Pat the chicken dry with a paper towel; season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 tablespoon oil until hot but not smoking. Add the chicken and cook, turning once, until browned and cooked through, 4 to 6 minutes per side, depending on thickness. Transfer to a plate to rest.
While the chicken cooks and rests, prepare the rest of the salad.

• Strip the kale leaves from the stems; finely chop the leaves.
• Juice the lime.

In a large bowl, massage the kale leaves with the lime juice and season with salt. Let stand for 5 minutes. Meanwhile, prepare the remaining ingredients.

• Trim the root end from the romaine; coarsely chop the leaves.
• Cut the chicken crosswise into ¼-inch-thick slices.
• Trim the root ends from the scallions; thinly slice the scallions on the diagonal.

To the bowl with the kale, add the soba noodles, romaine, carrots, and as much miso dressing as you like. Toss to coat and season to taste with salt and pepper.

Transfer the soba noodle salad to individual bowls. Top with the chicken, garnish with the scallions, and serve with any remaining dressing at the table.