Rice prep: use rice cooked the day before and refrigerated. Break up any clumps with your hands or a spatula before it hits the pan — cold clumps do not break down in the wok.
Heat 1 tbsp of the oil in a wok or large skillet over high heat until shimmering. Pour in the beaten eggs and scramble quickly, breaking into small soft pieces, about 30 seconds. Remove to a plate while still just set — they finish in the pan later.
Add the remaining 1 tbsp oil to the hot pan. Add the scallion whites and garlic (if using); stir-fry 30 seconds.
Add the rice, spreading it in an even layer. Let it sit undisturbed 30 seconds so the bottom crisps, then toss. Repeat twice until the grains are hot and a little toasty, about 3 minutes total. Do not crowd the pan — if your skillet is small, fry the rice in two batches; overloaded rice steams and turns gummy.
Push rice to the sides; pour the soy sauce into the cleared center so it sizzles for a few seconds, then toss everything together.
Return the eggs to the pan along with the scallion greens, white pepper, and sesame oil. Toss 1 minute until the eggs are fully set and everything is steaming hot. Serve immediately.