Step 1

Pat the swordfish dry on both sides. In a shallow dish just large enough to hold the swordfish in a snug, even layer, place the olive oil, soy sauce, vinegar, garlic, and oregano. Zest in both of the lemons, then juice 1 of the lemons into the marinade. Whisk to combine. Slice the second lemon in half crosswise and reserve for grilling.

Step 2

Add the swordfish steaks to the dish and turn to coat in the marinade. Let rest 10 to 15 minutes (do not let sit more than 20 minutes, or the acid will start to break down the fish). Halfway through, flip the swordfish over.

Step 3

Heat a gas grill or charcoal grill to medium-high (about 375 to 400 degrees F; you can also cook the fish under the oven broiler). Scrape the grill grates very clean, then oil to prevent sticking. Grill the swordfish for 4 to 5 minutes per side, just until it registers 135 degrees F on an instant read thermometer and is no longer pink in the center. Transfer to a plate and cover. Let rest 10 minutes.

Step 4

At the same time you are grilling the swordfish, grill the lemon halves by placing them cut-side down on the grill. Cook until char marks appear, about 6 minutes.

Step 5

Sprinkle the rested swordfish with herbs and a pinch of kosher salt. Squeeze the grilled lemon over the top. Enjoy hot.