Preheat grill to medium-high. In a mortar and pestle or spice grinder, smash cumin, paprika, 1 tsp. salt, garlic and chile until whole spices are cracked and garlic and chile are mashed. Stir in 2 Tbsp. oil. Place fish on a baking sheet; with a paring knife, make a few shallow slits in outside of flesh. Set 1 Tbsp. spice paste aside and rub fish all over with remaining paste. Stuff fish with lime slices.
Oil grill grates. Brush fish with 1 Tbsp. oil, place on grill and close cover. Grill, turning once, until flesh flakes easily when pierced and skin is charred and crisp, about 8 minutes per side. Transfer to a serving platter and let rest.
In a bowl, stir reserved spice paste with lime juice, parsley, cilantro, 1 Tbsp. water and remaining 2 Tbsp. oil. Spoon herb sauce over fish and serve.
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