Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
If using eggs, whisk them in a bowl and add them to the hot skillet. Scramble them until they're fully cooked but still slightly moist. Remove the scrambled eggs from the skillet and set them aside.
In the same skillet, add the remaining 1 tablespoon of vegetable oil. Add the chopped onion and sauté for 2-3 minutes until it becomes translucent.
Stir in the minced garlic and cook for another 30 seconds until fragrant.
Add the mixed vegetables to the skillet. Stir-fry for 3-5 minutes until they are tender-crisp.
Add the cooked and cooled rice to the skillet. Break up any clumps and stir-fry for 3-4 minutes until the rice is heated through and starts to turn slightly crispy.
Drizzle the soy sauce (and sesame oil, if using) over the rice and vegetables. Stir to combine evenly.
If you're using the scrambled eggs, return them to the skillet and stir them into the rice mixture.
Season with salt and black pepper to taste. Adjust the soy sauce and other seasonings as needed.
Add the chopped green onions and stir to incorporate them into the fried rice.
Once everything is heated through, remove the skillet from the heat.
Serve the Vegetable Fried Rice hot, garnished with fresh cilantro or parsley if desired.