Cut chicken to 1/2" pieces and marinate for 15 minutes with light soy sauce, sake, white pepper, salt and sesame oil.
SKIP THIS STEP IF YOU ARE USING STORE BOUGHT TERIYAKI SAUCE - Prepare your teriyaki sauce by combining light soy, mirin, sake, and sugar in a bowl and set aside.
Cut carrot, scallions, mushrooms, and cabbage to similar size pieces along with garlic and ginger and set aside.
In a pot of boiling water, cook udon noodles 2 minutes less than package directions and immediately drain and rinse with cold water.
Over high heat, cook chicken in 1 tbsp oil until cooked through and set aside.
Fry garlic and ginger for 15 seconds then add your vegetables and mix. Season with salt and continue cooking for another 1-2 minutes or until the vegetables are slightly wilted but still crisp.
Add back your chicken, udon noodles, and add your sauce and white pepper to taste. Continue cooking for 3-4 minutes over high heat until the sauce has thickened slightly. Top with sesame seeds and enjoy!