If you are using a charcoal grill, prepare and light it 30 to 40 minutes before you want to cook the fish.
If you are not cooking the fish over charcoal, put a ridged cast-iron grill pan over a high heat (or preheat the broiler). Brush the snapper fillets on both sides with olive oil and season well with salt and pepper. Cut each one into three, slightly on the diagonal.
Cook the pieces of snapper, either skin-side down on the grill or grill-pan, or skin-side up under the broiler, for 3 to 4 minutes.
To serve, spoon the salsa onto four plates and arrange the grilled strips of fish on top. Drizzle a little oil around the edge of the plates and garnish with cilantro sprigs.