Step 1: Heat 1 tablespoon of vegetable oil in a large wok or skillet over high heat. Add the diced chicken and cook until browned and cooked through, about 5-6 minutes. Remove chicken from the pan and set aside.
Step 2: Lower the heat to medium-high. Add a splash of oil if needed and pour in the beaten eggs. Scramble quickly until just set, then remove and set aside with the chicken.
Step 3: Add the remaining 1 tablespoon of oil to the wok. Sauté the onions, peas, and carrots for 3-4 minutes until softened. Stir in the garlic and ginger and cook for another 30 seconds until fragrant.
Step 4: Turn the heat back up to high. Add the cold rice to the wok, breaking up any large clumps with a spatula. Fry the rice for 2-3 minutes, tossing frequently.
Step 5: Pour the soy sauce and dark soy sauce over the rice. Stir well to ensure every grain is coated. Add the cooked chicken and eggs back into the pan.
Step 6: Toss everything together for 1-2 minutes until piping hot. Turn off the heat and stir in the toasted sesame oil and sliced green onions. Serve immediately.