Prepare a grill/pan for medium heat. Rub salmon with 2 Tbsp. olive oil; season both sides with salt.
Cut ends off lemon and discard. Place lemon upright and slice off outer lobes in 4 sections, leaving a square-shaped core and seeds behind. Finely chop lobes (flesh, pith, and all) and transfer to a small bowl (you should have about ⅓ cup). Squeeze out juice from core over bowl. Add shallot, sesame seeds, honey, sesame oil, and remaining ⅓ cup olive oil; season with salt and lots of pepper. Toss to combine.
Place salmon on grill/pan skin side down. Cover grill/pan and cook, skin side down the entire time, until skin is lightly charred and fish is opaque, 6–8 minutes. Transfer salmon to a plate and let cool slightly. (If using stove and pan, cover pan with top for same affect)
Divide salmon among plates. Top with basil. Spoon lemon-sesame sauce over.
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