Beat eggs with a whisk in a small bowl and season with salt and pepper, to taste. Heat very little oil in a medium frying pan over medium heat and make an omelette using half the beaten eggs. Turn out onto a plate to cool (do not fold omelette). Repeat process with remaining beaten eggs. Place 1 omelette on top of the other, fold and coarsely chop. Set aside.
In a medium bowl, toss chicken strips with the sesame oil and season with salt and pepper, to taste. Heat 3 tablespoons vegetable oil over high heat in large frying pan or wok and stir-fry the prepared chicken strips until lightly golden, about 2 to 3 minutes. Add the onion and garlic and stir-fry for 1 to 2 minutes or until onion has softened. Add 2 tablespoons more vegetable oil and when hot, stir in the cooked rice and green onions, tossing and mixing thoroughly until very hot. Sprinkle with soy sauce and mix evenly. Remove from heat and stir in chopped cooked egg. If desired, garnish with additional sliced green onions.