Cook the noodles in salted water according to the package instructions. Drain and rinse well under cold water. Add a drizzle of sesame oil and toss, to keep them from sticking.
While the pasta cooks, assemble the dressing. In a large bowl, whisk the tahini, honey, sesame oil, vinegar, garlic, and ginger together until smooth; season with salt and pepper.
Add the cold noodles, pepper, carrots, and cabbage to the bowl of dressing. Top with sesame seeds before serving. Dressed salad will keep well covered, in the refrigerator, for 4 days.