Prepare a charcoal or gas grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds).
Meanwhile, in a bowl, stir salsa with basil and 1 tbsp. mint. Season fish all over with olive oil, salt, pepper, and mint to taste. Set each fish skin-down on a double sheet of well-oiled foil.
Grill fish on foil about 3 minutes over a hot fire. Spoon salsa onto 2 plates and carefully slide fish off of foil onto salsa.