If cooking the rice, prepare according to package instructions. Cool and set aside. (This can be done up to day ahead).
Mix the soy sauce, fish sauce, sambal oelek and 1/4 cup water in a small bowl and set near the stove. Place all the remaining ingredients by the stove as well. Heat 1 tablespoon of the oil in a wok or large deep skillet over high heat. Add the eggs and cook, swirling the pan but not stirring the eggs, so the eggs spread out to make a flat, set omelet, about 2 minutes. Remove the omelet from the wok to the work surface, cool, and slice into strips.
Add 1 more tablespoon oil to the pan and, when hot, add the shrimp and cook, stirring, until just pink, about 3 minutes. Remove from the wok and chop coarsely. Wipe out any accumulated juices in the wok.
Reduce the heat to medium and add the remaining 1 tablespoon oil. Add the shallots, garlic, brown sugar and coriander and cook until the shallots are soft, about 2 minutes. Add the rice along with the soy sauce mixture and stir to coat and combine. Increase the heat to medium-high and continue stir-frying until the rice is heated through and lightly toasted, about 5 minutes. Stir in the shrimp and egg strips and cook until just heated through. Transfer to a platter and top with the drained scallions and carrots. Serve with more sambal oelek and hoisin, as desired.
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