Thirty to 40 minutes in advance, mix the salsa ingredients. Cover and reserve.
Preheat broiler. Brush salmon generously on all sides with the oil and season well with the salt and pepper. Place the onion slices on a sheet of foil, brush with the remaining oil, and season lightly with salt and pepper.
Place the fish in a broiling pan. On each portion, overlap 2 slices of the onion. Broil about 8 inches from the heat source until the onions have wilted and caramelized, 12 to 15 minutes. Don't worry if the onions char here and there, but if they blacken, cover them with foil. Check the fish for doneness: it should look rosy, not deeply salmon-colored.
When done, remove the fish to plates. Stir the reserved salsa and spoon it generously over the salmon.