Bring two large pots of salted water to a boil (one for the pasta, one for the chicken). Once boiling, add chicken, cover pot, and remove from heat. Set aside for 15 minutes to poach the chicken.
Add linguini to the other pot of boiling water and cook until al dente, 9-11 minutes.
Meanwhile, combine garlic, peanut butter, vinegar, 1 tbsp. sesame oil, soy sauce, chili oil, honey, vegetable oil and ¼ cup water in a small bowl. Whisk until combined.
Using two forks, shred the chicken.
Drain linguini and return to the pot, toss with the remaining 1 tbsp. sesame oil. Add shredded chicken, red cabbage and sauce mixture and toss to combine. Serve garnished with green onions and additional hot chili oil, if desired.