Step 1

Sprinkle mackerel with 1/4 teaspoon salt and 1/4 teaspoon pepper. Stir together extra-virgin olive oil and 3 tablespoons lemon juice in a small bowl. Place fish, skin side up, in a single layer in a shallow pan or dish. Pour marinade over fish; cover and chill 1 hour.

Step 2

Heat 1 tablespoon olive oil in a large cast-iron skillet over high. Working in batches, add fish, skin side down. Cook until golden brown, about 3 minutes; flip and cook until fish flakes easily with a fork and is cooked through, 30 seconds to 2 minutes depending on thickness. Remove from heat, and set aside.

Step 3

Cut tomatoes into wedges. Remove seeds; transfer seeds to a small bowl. Set tomato wedges aside. Add vinegar, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper to tomato seeds. Add lime juice, remaining 6 tablespoons olive oil, and remaining 3 tablespoons lemon juice; whisk until emulsified. Whisk in shallots and chervil until combined.

Step 4

Arrange fish and tomato wedges on 4 plates, and dress with vinaigrette.