In a medium bowl, toss the beef with 1 tablespoon soy sauce. In a large nonstick skillet, heat 2 tablespoons oil over medium-high heat. Add the beef and cook, stirring, for 2 minutes; transfer to a bowl.
In the skillet, heat 1 tablespoon oil over medium-high heat. Add the scallion whites, bell pepper and ginger and cook, stirring, for 2 minutes; stir in the peas. Push the vegetables to one side of the skillet, add 1 tablespoon oil and pour in the eggs. Stir the eggs until they begin to set, then stir in the vegetables. Add the egg-vegetable mixture to the beef; stir in the sugar and the remaining 1 tablespoon soy sauce.
Heat the remaining 2 tablespoons oil in the skillet over medium-high heat. Add the rice, breaking up any clumps, then cook, without stirring, until heated through, 2 minutes. Stir in the beef mixture and scallion greens.