1. Bring a large saucepan of water to a boil. Add soba; cook 3 minutes. Add broccoli to pan; cook 3 minutes or until soba and broccoli are done. Drain.
2. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Sprinkle chicken evenly with salt and pepper. Add chicken to pan; grill 6 minutes on each side or until done. Remove chicken from pan. Cut into 1-inch pieces.
3. Combine vinegar, sesame oil, soy sauce, peanut butter, 1 teaspoon sesame seeds, sugar, crushed red pepper, and garlic in a large bowl, stirring with a whisk. Stir in noodle mixture and chicken. Sprinkle with remaining 1 teaspoon sesame seeds and green onions.