In a large bowl, whisk together the peanut butter, soy sauce, rice vinegar, sesame oil, ginger and red pepper flakes.
Add the cooked and cooled soba noodles to the bowl and toss to evenly coat with the dressing. Add the cucumber, red pepper, carrots, and the white parts of the green onions, and toss to combine. Refrigerate for at least 1 hour before serving.
Serve and top with the reserved green parts of the green onion and sesame seeds, if desired. Leftovers can be stored in an airtight container in the refrigerator for up to 5 days.