Cook pasta in salted water according to package direction and drain well. Return the drained pasta to the dried original cooking pot and toss with 2 Tablespoons sesame oil. Put the lid on the pot to keep it warm and set aside.
Meanwhile, while the pasta is cooking, make the sauce; in a small bowl, whisk together cornstarch and water.Mix the remaining sauce ingredients except the lime, in a mixing bowl until smooth. Set aside
Add 1 tablespoon of the sesame oil to a large, high sided saute pan over medium heat. Add the carrots, cabbage, green onion and red pepper, and cook over medium-high until fork tender, about 5 minutes. Pour sauce into the skillet over veggies and bring to a simmer. Add chicken and simmer until chicken is heated through and sauce is nice and thick.
Pour sauce and veggie mixture over the pasta and toss until well combined. Squeeze lime juice over pasta, toss again, then pour the mixture into a serving dish and sprinkle the top evenly with cilantro and peanuts. Serve :)