Place the rice in a medium bowl and fill with water until covered by 1 inch. Stir the rice around with your fingers. Drain the water. Fill the bowl again halfway with cold water and let it sit at room temperature until the kernels soften, 20 to 30 minutes; drain.
In the meantime, heat the oil in a large lidded saucepan, Dutch oven, or casserole dish over a medium flame. Add the onion and 1/4 teaspoon turmeric and saute until translucent, about 5 minutes. Add the ginger, garlic, white parts of the scallions, and the chiles. Continue to cook for another 2 minutes, until very fragrant. Add the tomatoes and salt, and stir to combine. Simmer, stirring occasionally, until partially reduced, about 5 minutes.
In a medium bowl, toss the shrimp with half of the cilantro and the remaining turmeric. Season with salt and set aside.
Stir in the drained rice and the coconut milk. Simmer for 8 minutes, or until the liquid is nearly evaporated and the rice emerges. Stir once to scrape up the cooked rice from the bottom, and spread in an even layer. Cover and reduce the heat to the lowest possible setting. Cook for 8 more minutes, then arrange the shrimp in an even layer on top of the rice, cover, and let stand off the heat for 10 minutes.
Garnish with the remaining cilantro and the green scallions and serve family style, straight from the pan.