Preheat the oven to 375°F (190°C) and spray a 9x13-inch baking dish with nonstick spray.
Place the six salmon fillets in the prepared dish with space between each piece.
Drizzle the 2 tablespoons of olive oil over the fillets and top each fillet with one piece of the chilled butter.
Season the salmon generously with sea salt and freshly ground black pepper.
Bake the salmon for 13 to 16 minutes, or about 13–16 minutes depending on thickness, until cooked through and it flakes easily with a fork.
While the salmon bakes, combine the coconut milk, chili paste, grated ginger, lime juice, fish sauce, and brown sugar in a medium saucepan and bring to a boil.
Reduce heat to low and simmer, stirring often, until the sauce thickens slightly. Remove from heat.
When the salmon is done, spoon or drizzle the creamy coconut ginger sauce over each fillet and garnish with chopped chives, if desired.