Heat a large skillet over high heat until very hot, about 2 minutes. Add 1 tablespoon oil, eggs, and salt and cook until large curds set. Transfer the cooked eggs to a plate and tent to keep warm.
Reduce heat slightly and add the remaining oil, carrots, onions, and green onions. Cook until heated through (about 5 minutes, or until carrots are softened). Add garlic, and cook 1 more minute.
To the skillet, add the cold rice and cooked eggs.
Pour in melted butter, lemon juice, soy sauce, and frozen peas and cook, stirring frequently, for 3-5 minutes, or until heated through.
Season with salt and pepper to taste.