Combine the coconut milk, 2 teaspoons salt, ¼ teaspoon pepper, and 1 cup water in a medium saucepan and bring to a boil over high heat. Stir in the rice and bring back to a boil. Reduce the heat to medium-low, cover, and cook until the liquid has been absorbed and the rice is tender, about 18 minutes.
Remove the pan from the heat and let sit, covered, for 5 minutes. Remove the lid and fluff the rice with a fork. Spread the rice in an even layer over a large baking sheet and let cool completely, about 30 minutes. The rice can be made up to 24 hours in advance; store it on the baking sheet, covered with plastic wrap, in the refrigerator.
Combine the rice and scallions in a large bowl. Heat the oil in a large cast-iron or nonstick pan over high heat until it begins to shimmer. Add the rice and, using a heavy-duty metal spatula, immediately press the rice down into the pan until the top is flat. Cook, without stirring, until the bottom becomes golden brown and crispy, about 5 minutes (start checking at 4 minutes, making sure not to burn it). Turn the rice over and press down firmly on the top again. Cook until the bottom is golden brown and crispy, about 5 minutes more. Transfer to a platter, sprinkle with more scallions, and serve