Heat a large nonstick skillet or wok over high heat and then swirl in 1 tablespoon of the oil. When the oil begins to smoke, add the egg and swirl the skillet to make a flat egg pancake that's only half set, about 10 seconds; scoop out onto a plate.
Add the shrimp to the skillet, sprinkle with 1/4 teaspoon salt and cook, stirring constantly, until just cooked through, about 3 minutes. Transfer to a bowl. Add the remaining tablespoon oil, then add the watercress, carrots, peas, garlic, soy sauce, and 1/4 teaspoon salt and cook, stirring constantly, until the watercress wilts and the peas heat through, 2 to 3 minutes.
Add the rice, stirring to break up any clumps, and spread it out in the skillet. Cook until heated through, about 3 minutes. Return the egg, shrimp, and any juices to the skillet and cook, stirring and breaking up the egg, to mix it in thoroughly, about 1 minute. Season with additional salt if needed. Stir in the scallions and sesame oil and serve.
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