Marinate the chicken by combining soy sauce, sake, mirin, grated ginger, minced garlic, and cornstarch. Coat the chicken and refrigerate for at least 30 minutes.

Prepare the teriyaki sauce by combining soy sauce, mirin, sake, sugar, honey, ginger, and garlic in a saucepan. Heat until sugar dissolves and add a cornstarch slurry. Simmer until it thickens.

Cook the marinated chicken in a skillet over medium-high heat with vegetable oil, searing for 3-4 minutes per side until golden brown.

Cook noodles in boiling water according to package instructions, then drain and rinse under cold water.

Sauté bell peppers, onion, broccoli, and carrots in the same skillet until tender-crisp, adding minced garlic in the last 30 seconds.

Combine the cooked noodles and teriyaki sauce with the vegetables and sliced chicken, tossing for 2 minutes until heated through.

Serve warm, garnished with sesame seeds and green onions.