In a medium bowl, season the cubed chicken with salt and pepper. Add ¼ cup (of 60 ml) teriyaki sauce and mix until the chicken is well-coated. Cover with plastic wrap and marinate in the refrigerator for 30 minutes to 1 hour.
In a wok or deep skillet over medium-high heat, heat 2 tablespoons of cooking oil, then add the par-cooked noodles. Cook for 1-2 minutes, allowing the noodles to crisp, then flip and cook for another 1-2 minutes. Transfer to a plate and set aside.
In the same wok, heat 1 tablespoon of cooking oil, then add the chicken. Cook for 3-4 minutes, until browned on one side, then stir and cook for another 3-4 minutes, until fully cooked through. Set the chicken aside.
In the same wok, add 1 tablespoon of oil, the onion, and carrot. Cook for 2-3 minutes, or until the onions are translucent. Add the broccoli and cabbage. Stir and cook for 1-2 minutes, then season with salt and pepper and cook for 3 minutes more, until the vegetables are soft.
Add the cooked chicken and crispy noodles back to the wok, along with the remaining ¼ cup (60 ml) teriyaki sauce. Toss well and cook for 2-3 minutes, until everything is well-combined. Garnish with sesame seeds.