Heat a large skillet over high heat until very hot, about 2 minutes. Add half of the sesame oil, then pour in the beaten eggs and sprinkle with salt and white pepper. Cook, stirring gently, until large curds form and eggs are just set. Transfer to a plate and cover loosely to keep warm.

Reduce heat slightly and add the remaining sesame oil to the skillet. Add diced carrots, white onion, and green onions. Cook, stirring frequently, until vegetables have softened, about 5 minutes. Add minced garlic and cook for 1 more minute, just until fragrant.

Add the cooked and cooled rice to the skillet, breaking up any clumps with a spatula. Stir in the cooked eggs.

Pour in the melted butter, lemon juice, soy sauce, and frozen peas. Cook, stirring frequently, for 3–5 minutes, or until everything is heated through and evenly combined.

Season to taste with salt. Serve hot.