Mix the salt, turmeric and garlic together in a bowl. Sprinkle this mixture on top of the salmon fillet, and rub it in. Refrigerate the fish, covered, for 30 minutes or overnight, to allow the flavors to permeate the fish.
Heat oil in a large skillet over medium heat. Add the salmon fillet, spice-covered side down, and sear it for about 2 minutes. Turn the salmon over and sear the underside until browned, about 2 minutes.
Pour the coconut milk into a measuring cup, and add the peppercorns and chilies. Stir gently to mix. Pour the coconut milk sauce over the fish. Lift the fillet with a spatula and tilt the skillet slightly to allow the spiced coconut milk to run under it and release the browned bits of garlic, spice, and fish. Reduce heat to medium-low, cover the skillet, and braise the salmon, spooning the sauce over it occasionally, until the flesh is barely beginning to flake, 3 to 5 minutes.
Transfer the fish to a platter, spoon sauce over it, and serve.