Step 1

Preheat oven to 400°. Toast hazelnuts on a rimmed baking sheet, tossing occasionally, until golden brown, 6–8 minutes. Let cool.

Step 2

Pulse garlic, cilantro, parsley, capers, lemon zest, and ¼ cup hazelnuts in a food processor until finely chopped. With machine running, gradually add olive oil; season relish with salt. Coarsely chop remaining hazelnuts.

Step 3

Heat vegetable oil in a large ovenproof skillet over medium-high heat. Season salmon with salt and cook, skin side down, until skin is crisp (do not disturb), about 4 minutes. Add butter and cook, basting constantly, 1 minute. Transfer to oven and roast salmon, basting once, until medium-rare (mostly opaque but still slightly translucent in the center), about 3 minutes.

Step 4

Serve salmon, skin side up, with lettuce, topped with relish and chopped hazelnuts.

Step 5

DO AHEAD: Relish can be made 6 hours ahead. Cover and chill.

Step 6

Wine Pairing: Pick a wine that can match the brightness of the relish, like the Cristom 2013 Pinot Gris ($19).