How to Make It
Prepare soba noodles according to package directions. Add carrot during last minute of cooking. Drain; rinse with cold water. Drain.
Combine oil and next 6 ingredients (through honey) in a large bowl, stirring with a whisk. Place 2 tablespoons miso mixture in a medium bowl. Add noodle mixture, cabbage, and green onions to remaining miso mixture; toss to coat. Sprinkle with sesame seeds.
Sprinkle chicken with pepper and salt. Add chicken to reserved 2 tablespoons miso mixture, turning to coat. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Add chicken to pan; cook 3 minutes on each side or until done. Serve with noodle mixture.