Step 1

In a large saucepan, rinse the rice, then drain it. Return the rice to the saucepan, add the water and bring to a boil. Cover the saucepan and cook the rice over low heat until the water is absorbed, about 15 minutes. Stir in the shredded coconut, cover and let stand off the heat for 10 minutes. Fluff the rice and spread it out on a large rimmed baking sheet. Let cool, then refrigerate, uncovered, until completely chilled, about 1 hour.

Step 2

Meanwhile, in a small bowl, toss the onion with the vinegar and a large pinch of salt. Let stand for 10 minutes.

Step 3

In a small saucepan of boiling water, cook the carrots until tender, about 6 minutes. Drain and set aside.

Step 4

In a medium nonstick skillet, heat 1 tablespoon of the vegetable oil. Season the eggs with salt. Add them to the skillet and cook over moderate heat, stirring a few times, until just scrambled, about 1 minute. Transfer the eggs to a large plate.

Step 5

Wipe out the skillet and heat 3 tablespoons of the vegetable oil in it. Add the sliced shallots and cook over moderately high heat, stirring frequently, until they're browned and crisp, about 2 minutes. Using a slotted spoon, transfer the shallots to a small bowl. Add the shrimp to the skillet and season with salt and white pepper. Cook over moderate heat, turning once, until just cooked through, about 2 minutes. Add the shrimp to the plate with the eggs.

Step 6

Rub the cooked rice between your hands to separate the grains. In each of 2 large skillets, heat 3 tablespoons of vegetable oil. Add half of the cabbage and crushed red pepper to each skillet and stir-fry over moderately high heat until softened, about 3 minutes. Add half of the peas, carrots and pickled onion to each skillet and stir until hot.

Step 7

Add half of the rice to each skillet along with the shrimp and eggs and toss over moderate heat until well mixed and heated through, about 2 minutes. Remove from the heat and stir half of the fish sauce into the rice in each skillet. Season with salt and pepper. Transfer the rice to a large bowl, garnish with the fried shallots and serve.