Light the barbecue, adjusting one side to high heat and the other to low heat to better control the temperature.
Using a sharp knife, make small incisions about 1 cm deep on both sides of each fish. This will help the flavors penetrate the fish and allow the heat to cook the fish evenly.
On a large cutting board, coarsely chop the oregano leaves, then sprinkle them generously with sea salt and black pepper. Roll the fish in the mixture to coat the incisions with the spices.
Place the fish on the hotter side of the barbecue to give them some color. The salsa will be made on the cooler side or on a ring. Simply heat the olive oil in a pan, add the chopped olives, and heat for about 1-2 minutes. Add the garlic, red pepper, and rosemary sprigs, mix well, and cook while the fish continues to cook.
After about 4 minutes, flip the fish over, loosening them from the grill with a spatula – be patient, or they will stick – and cook for another 4 minutes, until the interior is cooked and moist and the exterior is crispy.
Remove and discard the rosemary sprigs from the pan, as they will have released their flavor. Add the chopped tomatoes to the pan and mix. Squeeze the lemon juice and add the chopped parsley. Season the salsa to taste. The olives are usually very salty, so adding salt may not be necessary, but it’s up to taste. Add some black pepper. Once everything is heated through, remove the pan from the heat.
Place the fish on a plate. To ensure they are cooked, pull off a piece of flesh. If it comes off easily, it’s cooked.
Serve the fish simply with the salsa on top.
If there are leftovers, it’s possible to remove the flesh from the bones and flake it into a bowl. Mix with the remaining salsa, add some chopped parsley or arugula, and serve with good bread.