The secret to the maxed-out flavor of this coconut brown rice dish? Coconut in three forms—milk, oil and shredded.
Heat oil in a medium saucepan over medium heat. Add shallots and cook, stirring often, until starting to brown, 4 to 6 minutes. Add coconut and cook, stirring often, until golden brown, about 2 minutes. Transfer to a plate with a slotted spoon and sprinkle with a pinch of salt.
Add rice to the pot and stir to coat. Add coconut milk, water and the remaining 1/2 teaspoon salt. Bring to a boil. Reduce heat to maintain a low simmer, cover and cook until the rice is tender and most of the liquid is absorbed, 40 to 45 minutes. Remove from heat and let stand, covered, for 10 minutes. Fluff with a fork. Serve the rice topped with the toasted coconut and shallots.