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1
Place the butter in a medium bowl and mash it with a rubber spatula until its very spreadable.
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2
Add the zest, garlic, and measured salt and pepper and mix until thoroughly combined.
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3
Transfer the butter mixture to a sheet of plastic wrap.
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4
Shape it into a log by rolling it up in the plastic wrap, then twist the ends and fold under to seal.
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5
Place in the refrigerator to harden before using, at least 30 minutes.
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6
Cut the zested lemons in half and set them aside.
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7
Heat a grill pan or outdoor grill to medium high (about 375 degrees F to 425 degrees F).
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8
Pat the salmon dry with paper towels.
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9
Coat both sides of the fillets with oil and season generously with salt and pepper.
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10
When the grill is ready, rub the grates with a towel dipped in the vegetable oil.
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11
Place the salmon on the grill skin-side down, cover the grill, and cook undisturbed until grill marks appear and the skin is starting to crisp, about 2 to 3 minutes.
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12
Using a flat spatula, carefully flip the fillets over.
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13
Place the reserved lemons cut-side down on the grill.
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14
Cover the grill and continue to cook until the salmon is just opaque in the center and the lemons have grill marks, about 2 to 4 minutes more.
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15
To serve, cut 4 (1/4- to 1/2-inch-thick) rounds of the lemon-pepper butter (you will have some left over).
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16
Immediately place a round on top of each piece of fish and serve with the grilled lemon halves to squeeze over the salmon.