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Marinate the swordfish (optional) with lemon juice, thyme sprigs, peppercorns for 10 to 15 minutes.
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While the swordfish marinates, prepare the charcoal grill for high-heat grilling.
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Brush the fish with oil (if not marinated) and season on all sides with Kosher Salt and freshly ground pepper.
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Grill for 3 to 8 minutes per side, or until internal temperature reaches 140° F. The fish should be browned on the outside and still slightly pink on the inside.
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Melt the butter in a small pan on the grill until it starts to turn golden brown, 3 to 4 minutes.
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Move it off the heat and carefully add lemon juice and swirl to combine.
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Once you turn the fish over, begin brushing some of the lemon-butter onto the cooked side as it finishes grilling.
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Serve the swordfish with a drizzle of the lemon-butter, a sprinkle of coarse salt and a lemon slice.