Heat 1 tablespoon of sesame oil in a large skillet or wok over medium-high heat.
Add the diced chicken breast to the skillet and season with salt and pepper. Cook until fully cooked and golden brown, about 5-7 minutes. Remove the chicken from the pan and set aside.
In the same skillet, add the minced garlic and ginger. Sauté for about a minute until fragrant, then add the mixed vegetables. Cook for another 2-3 minutes until the vegetables are tender.
Push the vegetables to one side of the skillet and pour the beaten eggs into the other side. Scramble the eggs until cooked, then mix with the vegetables.
Add the cooked rice to the skillet and toss everything together. Drizzle in the teriyaki sauce and soy sauce, and mix until the rice is evenly coated.
Add the cooked chicken back to the skillet and stir-fry for an additional 2-3 minutes, allowing flavors to meld.
Finally, sprinkle chopped green onions on top and stir well. Adjust seasoning with more soy sauce or salt if needed.
Remove from heat, garnish with sesame seeds, and serve hot.