Combine the rice with 4 cups lightly salted water in a large saucepan and heat to boiling. Reduce heat to low, cover, and simmer gently 25 to 30 minutes or until all the water is absorbed.
Heat 2 tablespoons of the oil over medium-high heat in a large skillet, wok, or saucepan. Add the eggs and cook through, stirring to break up into small pieces. Remove and set aside.
Heat the remaining oil in the skillet and add the onion and carrot and cook until the onion is golden, about 2 minutes. Add the peas and scallions and cook about 2 minutes more to heat through.
Stir in the tomato, salt, cooked rice, and eggs and toss until heated through. Fold in the basil.