In a small bowl, whisk together the soy sauce, sesame oil, oyster sauce (if using), and sugar. Set aside.
Heat 1 tablespoon of vegetable oil in a wok or large skillet over medium-high heat. Add the diced chicken and cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove from the pan and set aside.
In the same pan, add the remaining tablespoon of vegetable oil. Add the minced garlic and ginger and cook for 1 minute until fragrant. Add the mixed vegetables and cook for another 3-4 minutes, until they are tender and heated through.
Push the vegetables to the side of the pan. Crack the eggs into the empty side of the pan and scramble them, cooking for about 2-3 minutes. Once scrambled, combine them with the vegetables.
Add the day-old rice to the pan, breaking up any clumps. Add the cooked chicken back into the pan as well. Pour the sauce over the rice mixture and stir everything together to coat evenly. Cook for another 3-4 minutes, until everything is well combined and heated through.
Stir in the sliced green onions and remove the pan from heat. Serve hot.