In a bowl, combine the EVOO, garlic and a pinch each salt and pepper; let steep for 30 minutes. Strain the oil; discard the garlic. in a small bowl, whisk together 1 cup of the garlic oil, the lemon juice, parsley and mint; season with salt and pepper.
Preheat a large cast-iron or nonstick skillet over medium-high heat. Place the fish fillets in a shallow dish in a single layer. Sprinkle with 2 tsp. salt and drizzle with the remaining 1/2 cup garlic oil, turning the fillets gently to coat.
Working in batches if necessary to avoid overcrowding, add the fish, flesh side down, to the hot skillet. Cook, turning once, until the fish is just opaque in the center, 6 to 8 minutes, depending on the thickness of the fish. Transfer to a plate.
Spoon a little of the sauce over each fillet. Set the rest of the sauce on the table for passing.