Step 1: Heat 1 tablespoon of vegetable oil in a large wok or a very large non-stick skillet over medium-high heat until shimmering. Pour in the whisked eggs.
Step 2: Let the eggs set for a few seconds, then gently scramble them until just cooked through but still soft. Remove the scrambled eggs from the pan and set aside on a plate.
Step 3: Add another 1 tablespoon of vegetable oil to the same wok/skillet and increase the heat to high. Add the minced garlic and grated ginger (if using). Stir-fry for about 30 seconds until fragrant.
Step 4: Add the finely diced onion and carrot to the wok. Stir-fry for 2-3 minutes until they begin to soften. Add the thawed frozen peas and corn (if using) and stir-fry for another minute.
Step 5: Add the cold, day-old rice to the wok. Break up any clumps with your spatula. Spread the rice evenly in the pan and let it sit undisturbed for about a minute to get a slight char on some grains. Then, stir-fry vigorously for 3-5 minutes, ensuring the rice is heated through and slightly toasted.
Step 6: Push the rice and vegetables to one side of the wok, creating a small clearing. Add the remaining 1 tablespoon of vegetable oil to the clearing. Pour in the soy sauce, sesame oil, and granulated sugar mixture. Let it bubble for 10-15 seconds, then quickly toss and mix it into the rice until everything is evenly coated and beautifully colored.
Step 7: Return the scrambled eggs to the wok. Add most of the thinly sliced green onions (reserve a small amount for garnish). Toss everything together gently for another minute, just until the eggs are fully incorporated and heated through.
Step 8: Remove from heat immediately. Taste and adjust seasoning if necessary. Serve hot, garnished with the reserved green onions.