Preheat your oven to 400°F (200°C). This ensures that the salmon cooks evenly and comes out flaky.
Place the salmon fillets on a baking sheet lined with parchment paper. Drizzle with olive oil and season generously with sea salt and freshly ground black pepper.
In a mixing bowl, combine the canned coconut milk, chili paste, grated fresh ginger, freshly squeezed lime juice, fish sauce, and brown sugar. Whisk until smooth and well combined.
Place the baking sheet in the preheated oven and bake for about 12-15 minutes, or until the salmon is cooked through and flakes easily with a fork.
Remove the salmon from the oven and spoon the creamy coconut ginger sauce generously over each fillet. Top each piece with a piece of chilled salted butter, allowing it to melt into the sauce.
Sprinkle with chopped chives for a fresh finish, then serve immediately. Pair this dish with rice or steamed vegetables for a complete meal.