Cook pasta to al dente, according to package directions. When pasta is 3 minutes from completely cooked, add carrot matchsticks. Drain and place back in pot or a large serving bowl.
Mince ginger.
Add broth, peanut butter, vinegar, soy sauce, ginger and sriracha sauce to a mixing bowl. Whisk together until smooth. Pour over pasta and carrots.
Shred 2 cups of chicken from rotisserie and add to pasta; toss to combine and evenly coat.
Serve pasta topped with sliced onions and sesame seeds, and sliced peaches on the side.