In a medium saucepan, bring water to a boil and cook soba noodles according to the package directions.
Drain and rinse the noodles in a colander under cold running water and set aside.
In a large bowl, whisk together the red miso paste, rice vinegar, apple cider vinegar, toasted sesame seeds, ginger, honey, and toasted sesame oil to make the dressing.
Add the drained soba noodles, sliced cucumber, and torn red-leaf lettuce into the dressing bowl. Gently toss until well coated in the dressing.
To serve, twirl the noodles using tongs and set them in individual serving bowls. Top with avocado slices, poached egg slices, toasted sesame seeds, and nori strips if desired.