Cook your rice (see instructions here).
Pat the salmon filets dry, especially the skins (this will help them get crispy). Sprinkle the skins with ½ teaspoon salt and rub it all over the skin.
In a large skillet add 1 tablespoon oil and use a spatula to coat the pan in the oil. Place the filets in the skillet, skin-side-down, then turn the heat to medium-high. Sprinkle the salmon flesh with ½ teaspoon salt. Cook until the salmon is almost all the way cooked through and the skin is crispy, about 7 minutes (see tip!). Transfer the salmon to a plate, skin-side-up. We will finish cooking it later.
Add the remaining 1 tablespoon oil to the skillet along with the carrots, white/light green parts of the scallions, and remaining ¼ teaspoon salt. Cook until the carrots have softened a bit, about 2 minutes.
Stir in the curry powder for 30 seconds, stirring constantly, then immediately stir in the coconut milk and soy sauce. Stir the greens into the coconut milk until they wilt down a bit (about 30 seconds), then nestle the salmon filets back into the skillet, skin-side-up. Bring the liquid to a simmer and cook until salmon is cooked through, about 4-8 more minutes.
Drizzle the lime juice into the coconut milk (not onto the salmon) and give the pan a shake or gentle stir to mix it in.
Serve over rice (or base of choice) and top with the green parts of the scallions, nuts, and another squeeze of lime.