Cook the bowtie pasta in a large pot of salted water according to package directions until al dente. Drain and rinse under cold water to stop the cooking.
In a large mixing bowl, whisk together the sesame oil, soy sauce, rice vinegar, honey, grated ginger, and minced garlic until smooth.
Add the cooled pasta and shredded chicken to the bowl with the dressing. Toss to coat evenly.
Stir in the shredded carrots and sliced green onions. Sprinkle the sesame seeds over the top and toss once more.
Cover and refrigerate for at least 30 minutes before serving to let the flavors settle.