Begin by heating the vegetable oil in a large non-stick skillet or wok over medium-high heat. Ensure the oil is hot but not smoking.
Crack the eggs into a medium bowl and whisk them briefly until combined. Pour the whisked eggs into the hot skillet. Scramble the eggs gently for about 1-2 minutes until they are just set. Remove the scrambled eggs from the skillet and transfer them to a plate, leaving any residual oil in the skillet.
In the same skillet, add the sesame oil. Once it heats up, add the mixed vegetables. Stir-fry for about 2-3 minutes, or until the vegetables are tender yet still retain a slight crispness.
Incorporate the cooked jasmine rice into the skillet, breaking up any clumps as you stir. Stir-fry the rice for approximately 2 minutes, ensuring it is heated through and starts to fry slightly.
Return the scrambled eggs to the skillet, mixing them thoroughly with the rice and vegetables.
Drizzle the soy sauce over the mixture, stirring well to ensure that the rice is evenly coated. Adjust seasoning with salt and pepper to your taste.
Add the chopped green onion whites to the skillet, stirring them in just before serving to retain their freshness.
Serve your Egg Fried Rice hot, garnished with a sprinkle of toasted sesame seeds and fresh cilantro, if using.