Step 1

Prepare a grill for medium heat. Rub salmon with 2 Tbsp. olive oil; season both sides with salt.

Step 2

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.

Step 3

Clean and oil grate, then immediately place salmon on grill skin side down. Cover grill 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.

Step 4

Divide salmon among plates. Top with basil. Spoon lemon-sesame sauce over.