Preheat the oven to 375 degrees Fahrenheit / 190 degrees Celsius. Rinse the rice in a fine-mesh strainer under cold water until the water runs mostly clear, then drain it very well.
1 cup Jasmine rice
Pat the salmon dry very well with paper towels. Season all over with the 1 teaspoon kosher salt and the black pepper.
4 skinless salmon fillets, 1/2 teaspoon black pepper, 1 teaspoon kosher salt
Heat the neutral oil in a large oven-safe skillet over medium-high heat. Once the oil is shimmering, add the salmon flesh-side down. Cook for 3 to 4 minutes, until the salmon has a deep golden crust and releases easily from the pan. Flip and cook for 30 seconds on the second side, then transfer to a plate. The salmon should not be cooked through at this point.
2 tablespoons neutral oil, 4 skinless salmon fillets
Reduce the heat to medium. Add the shallot and cook for 2 to 3 minutes, stirring often, until softened and lightly translucent. Add the garlic and ginger and cook for 30 seconds, just until fragrant.
1 medium shallot, 4 to 5 garlic cloves, 1 tablespoon finely grated fresh ginger
Add the drained rice and stir for 1 to 2 minutes, until the grains look glossy and lightly toasted.
1 cup Jasmine rice
Pour in the coconut milk and water, scraping up any browned bits from the bottom of the pan. Stir in half of the lime zest and the 3/4 teaspoon kosher salt. Bring the mixture to a gentle simmer over medium heat.
3/4 teaspoon kosher salt, 1 13.5 ounce can full-fat coconut milk, 2/3 cups water, 2 limes
Cover the skillet tightly with a lid or foil and transfer it to the oven. Bake for 15 minutes, until the rice is mostly cooked and most of the liquid has been absorbed.
Remove the skillet from the oven and uncover it. The rice may still look a little loose on top, but it should no longer look wet or soupy. If it seems dry and the rice is still a little firm, add a small splash of water. Nestle the salmon back into the rice along with any juices from the plate.
4 skinless salmon fillets
Return the skillet to the oven uncovered and bake for 6 to 8 minutes more, until the rice is tender and the salmon is cooked to your liking. The salmon should look opaque around the edges and gently flake when pressed with a fork.
Let the skillet rest for 5 minutes. Finish with the lime juice, the remaining lime zest, and the scallions. Taste and add a little more salt if needed, then serve.
2 limes, 4 scallions, 2 limes