Ingredients

3 pounds 1-inch-thick swordfish steaks, cut into 8 pieces

Salt and freshly ground black pepper

1/2 cup plus 1 tablespoon extra-virgin olive oil, plus more for brushing

1/4 cup pitted oil-cured olives

1 small clove garlic, peeled

1 1/2 cups loosely packed arugula leaves

1/4 cup fresh flat-leaf parsley leaves

1/4 teaspoon dried oregano

12 small leeks, well washed

Preparation

Arrange swordfish steaks in a shallow baking dish, season well with salt and pepper, and coat with 3 tablespoons olive oil. Let marinate at room temperature for up to 1 hour, until ready to grill. (Or marinate longer in the refrigerator, and return fish to room temperature before grilling.)

Heat a grill or grill pan until very hot. Meanwhile, to make pesto, combine olives, garlic, arugula, parsley, oregano, and salt to taste in the bowl of a food processor. With machine on pulse, slowly add remaining 6 tablespoons olive oil. Add 1 1/2 tablespoons hot water, pulsing, until coarsely pureed. Set aside.

Place fish and leeks on grill. Cook for about 5 minutes; remove leeks from grill, then turn fish. Cook fish for another 5 minutes or until nearly cooked through; remove from grill, and transfer to a shallow serving dish.

Arrange leeks on a serving platter, and place fish on top. Spoon pesto over hot fish, turning fish to coat well. Pour juices over fish, and serve.