Simmer rice, its water, and salt in deep 12-inch skillet. Cover tightly; cook over low 17 to 19 minutes until water absorbed and rice tender. Remove from heat; rest covered 10 minutes.
Spread rice shallowly on large plate; promptly refrigerate about 60 minutes to 40°F or colder, included in prep time. Wipe skillet dry.
Heat 1 teaspoon neutral oil over medium. Scramble eggs 1 to 2 minutes until fully set; transfer to bowl.
Add 1 tablespoon neutral oil; raise to medium-high. Cook chicken, carrot, and scallion whites 7 to 8 minutes, crumbling chicken finely, to 165°F. Add garlic and ginger 30 seconds.
Add remaining neutral oil and cold rice; spatula-break clumps. Spread across skillet; cook 4 to 5 minutes, turning every minute, until grains hot and separate.
Add peas, soy sauce, oyster sauce, and white pepper; stir-fry 2 to 3 minutes until peas hot. Fold in eggs, scallion greens, and sesame oil; cook 1 minute to 165°F throughout. Serve 4 portions.