Stir together soy sauce, oyster sauce, rice vinegar, sesame oil, and white pepper; set aside.
Break up the cold rice with your hands to separate any clumps.
Heat a large skillet or wok over medium-high. Add 1 tablespoon oil.
Pour in beaten eggs. Soft-scramble until just set, then transfer to a plate.
Add remaining oil. Crumble in beef and cook, stirring, until browned. Drain excess fat if needed.
Stir in onion and carrots. Cook until slightly tender, about 3 minutes.
Add garlic and ginger. Stir-fry until fragrant, about 30 seconds.
Toss in peas and the white parts of the green onions. Cook 1 minute.
Add rice. Stir-fry, pressing rice against the pan to sear lightly, 2–3 minutes.
Pour the sauce around the pan. Toss until rice is evenly coated and glossy.
Return eggs. Add butter and the green onion tops. Toss and adjust seasoning to taste.