While pasta cooks, make the peanut sauce: In a small bowl, whisk together garlic, honey, peanut butter, soy sauce, rice vinegar, and ginger.
Drain pasta and toss with 1 Tbsp. sesame oil to keep from sticking. Set aside.
Wipe out pasta pan and heat the other 1 Tbsp. sesame oil on medium heat. Add carrots and saute until tender, about 5 minutes. Add cabbage and green onions and saute another minute or two until the cabbage begins to soften.
Add the pasta back to the pan, along with the chicken and peanut sauce. Stir well to combine and continue cooking on low until heated through.
Garnish with additional green onion slices, peanut pieces, and/or sesame seeds. Serve immediately.