Separate egg yolks from whites, placing yolks in a medium bowl and whites in a small bowl. Add rice to bowl with yolks and mix to break up any clumps and coat each grain with yolks (take your time with this as any clumps will cook together); set aside.
Stir 2 Tbsp oil into egg whites and season lightly with salt. Heat a dry large nonstick skillet over high. Add egg white mixture and cook, pushing around constantly with chopsticks or a heatproof rubber spatula, until gently set, about 30 seconds. Transfer to a plate. Wipe out skillet if needed.
Heat 2 Tbsp. oil in skillet over medium-high. Add ginger, stirring, until very fragrant, about 20 seconds. Add yellow onion, season with a pinch of salt. Cook, stirring, until onion is translucent, about 1 minute (remove from heat if onion starts to go past golden brown). Add reserved rice mixture, sprinkle with sugar, and season with salt. Toss to combine, then cook, undisturbed, until rice is beginning to warm and crisp underneath, about 1 minute.
Push some of the rice to the side to clear a few inches in skillet. Drizzle a bit of oil into the clearing. Add scallion white and pale green parts and garlic and cook, stirring, until just softened and fragrant, about 45 seconds. Toss into rice mixture and cook, tossing occasionally, until warmed through and rice is crisp and chewy, about 3 minutes. Return cooked egg whites to pan and cook, tossing and breaking up with spatula until distributed.
Now is when you would add extras...veggies, protein, and then condiments. Stir fry additional minute to combine and heat through.
Special Shout Out to my favorite: catsup or ketchup, add it now. Start with at least 2-3 tablespoons and then add to taste. Fry to heat and incorporate catsup throughout the rice.
Divide among plates and top with scallion greens.