For the dressing: Grate the ginger into a deep bowl (large enough to hold the salad ingredients). Add the olive oil, sesame oil, peanut butter, honey, mustard, soy sauce and lime juice. Season the dressing with salt and pepper. Whisk together until emulsified, about 1 minute.
For the salad: Add the spaghetti, carrots, peppers, scallions and cilantro to the bowl. Using tongs, toss until the noodles are coated with the dressing. Cover the bowl, and marinate for at least 30 minutes and up to overnight, so the noodles can absorb the flavors from the dressing.