Step 1

For the best results, purchase swordfish steaks that are 1 to 1½ inches thick. Look for two steaks that weigh 7 to 9 ounces each or one steak that weighs about 1 pound. If you purchase the latter, cut it in half to create two steaks. Ask your fishmonger to remove the skin or trim it yourself with a thin, sharp knife.

Step 2

Whisk oregano, lemon zest and juice, garlic, ¾ teaspoon salt, and ¼ teaspoon pepper in bowl until salt is dissolved. Whisk in oil.

Step 3

Arrange swordfish in single layer in shallow pan or dish. Pour half of marinade over fish, flipping steaks to ensure both sides are evenly covered. Refrigerate for at least 20 minutes or up to 45 minutes. Whisk 2 teaspoons parsley into remaining marinade and set aside.

Step 4

FOR A CHARCOAL GRILL:  Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.

Step 5

FOR A GAS GRILL:  Turn all burners to high; cover; and heat grill until hot, about 15 minutes. Leave primary burner on high and turn other burner(s) to medium-high.

Step 6

Clean and oil cooking grate. Remove fish from marinade, letting excess drip off (do not pat dry). Sprinkle both sides with remaining ¼ teaspoon salt and ¼ teaspoon pepper. Place fish on hotter side of grill and cook (covered if using gas), flipping every 2 minutes, until steaks develop dark grill marks and register 130 to 135 degrees, 7 to 11 minutes.

Step 7

Transfer fish to clean shallow pan or dish and pour reserved marinade over top. Tent with aluminum foil and let rest until centers register 140 degrees, 5 to 10 minutes. Transfer fish to serving platter or individual plates and sprinkle with remaining 1 teaspoon parsley. Transfer sauce in pan to small bowl. Serve, passing sauce separately.