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Combine the water, rice, and 1/4 teaspoon of salt in a rice cooker and cook according to the manufacturer's instructions.
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Transfer the steamed rice to a baking sheet to cool to room temperature. Cover and refrigerate until cold.
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Heat 1 tablespoon of canola oil in a large wok over medium-high heat.
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Add the eggs and stir with a fork for about 30 seconds or until just cooked.
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Remove the eggs from the wok and set aside on a plate.
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Heat the remaining 3 tablespoons of canola oil in the wok over medium-high heat.
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Add the carrots to the wok and stir fry for 2 minutes.
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Add the cold rice and stir fry for 2 minutes or until heated through.
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Season with salt and pepper.
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Stir in the eggs and 3/4 of the green onions.
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Add the soy sauce and sesame oil and continue to stir fry for 1 minute.
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Transfer the rice to a bowl and sprinkle with the remaining green onions.