To season the shrimp, in a bowl, add the shrimp, salt, white pepper, and cornstarch and mix until evenly coated, then add the cooking oil and toss gently to combine.
To make the sauce, in a bowl, combine the soy sauce, sake, mirin, and sugar and mix until the sugar is dissolved.
To prepare the rice, loosen the overnight rice with your hands so the grains separate easily before cooking.
To stir-fry the shrimp, in a wok over high heat, add 1 tablespoon of cooking oil, add the shrimp and garlic, and stir-fry for about 1 minute until just pink, then remove.
To stir-fry the vegetables, in the same wok over high heat, add 1 tablespoon of cooking oil, add the onion and carrot and stir-fry for about 30 seconds until fragrant, then remove.
To cook the eggs and rice, in the wok over high heat, add the remaining 1 tablespoon of cooking oil, add the eggs and scramble until partially set, then add the rice and stir-fry until heated through and the grains are separated.
To combine, return the shrimp and vegetables to the wok, pour in the sauce and toss quickly until evenly coated, then add the scallions and give a final toss.
To serve, transfer to a plate and serve hot.