Bring a large pot of salted water to boil. Once boiling, add the soba noodles. Cook for 3-5 minutes until tender, then drain and set aside.
Combine granulated garlic, ginger, sesame oil, brown sugar, soy sauce, and rice vinegar in a small saucepan over medium heat. Whisk until sugar has dissolved. Combine cornstarch with 1/4 cup (1/2 cup for 4 servings) of cold water and whisk until smooth. Stir cornstarch mixture into the sauce and heat gently until thickened. Set aside.
Heat a drizzle of oil in a large skillet over medium, and add chicken. Season with salt and pepper, and cook for 3-4 minutes until no longer pink on the outside. Break apart any large pieces of chicken with your spatula. Cover the skillet and continue to cook the chicken.
While chicken is cooking, wash and break apart the broccoli florets, wash and slice red bell pepper into 1/4 inch strips. Thinly slice the green onion. Add broccoli and red bell peppers to the skillet and cover with the lid to allow the vegetables to steam until tender crisp. Toss with the prepared teriyaki sauce to coat.
Cut the lime into wedges. Divide soba noodles between serving dishes and top with vegetables and chicken. Garnish with green onion, sesame seeds and lime wedges. Enjoy!