In a medium bowl, marinate the diced chicken breast with 1/4 cup of teriyaki sauce for at least 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Sauté the minced garlic for about 30 seconds until fragrant.
Add the mixed vegetables to the skillet and cook for 2-3 minutes, stirring frequently until they are tender.
Push the vegetables to one side of the skillet and pour the beaten eggs into the other side. Scramble the eggs until fully cooked, then mix them with the vegetables.
Add the cooked rice to the skillet, breaking up any clumps. Pour in the remaining teriyaki sauce and stir well to combine all ingredients.
Return the cooked chicken to the skillet and mix everything thoroughly. Cook for an additional 2-3 minutes to heat through and allow the flavors to meld.
Season with salt and pepper to taste. Add sliced green onions just before serving, reserving some for garnish.
Serve hot, garnished with sesame seeds and additional green onions if desired.