Step 1

Rub 1 tablespoon of the oil all over the halibut fillets, then lightly season them with salt and pepper.

Step 2

In a shallow serving bowl large enough for the fish, stir together the remaining 3 tablespoons of oil, the lime juice, vinegar, olives, garlic, olive brine, onion, bay leaf, if using, chile, if using, and cilantro.

Step 3

Heat a well-seasoned grill pan or large cast-iron skillet over medium-high heat until it just begins to smoke. Place the fillets skin side down in the hot pan and cook until the skin turns golden brown, 4 to 6 minutes. Carefully flip and cook until the flesh is opaque and the fish begins to flake when prodded with a fork, another 4 to 6 minutes.

Step 4

Nestle the fish into the bowl with the vinegar mixture, skin side up, and let marinate for at least 15 minutes and up to 40 minutes (the longer it marinates, the more pungent its flavor will be).

Step 5

Transfer each fillet to a shallow bowl and spoon the sauce over. Discard the bay leaf. Serve warm or at room temperature, with rice or plantain chips on the side, if desired.