Combine the tamari, sweet chili sauce, vinegar, ginger, sesame oil, and ¼ of the green onions. Set aside.
Prepare the noodles according to the package directions. Let cool.
Combine the carrots, mint leaves, basil leaves, and roasted cashews.
Assemble the salads by placing the noodles at the bottom of four bowls. Arrange the shrimp, herb salad, cucumber, and pepper slices in segments on top of the noodles. Sprinkle with the remaining green onions and sesame seeds. Serve with the dressing.