½ cup blanched hazelnuts
1 garlic clove, chopped
1 cup (packed) fresh cilantro leaves with tender stems
½ cup (packed) fresh flat-leaf parsley leaves with tender stems
1 tablespoon capers
1 teaspoon finely grated lemon zest
½ cup olive oil
1 tablespoon vegetable oil
4 6-oz. pieces skin-on salmon fillets
2 tablespoons unsalted butter, cut into pieces
2 heads Little Gem or other small lettuce, leaves separated
Preheat oven to 400°. Toast hazelnuts on a rimmed baking sheet, tossing occasionally, until golden brown, 6–8 minutes.
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.
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.
Serve salmon, skin side up, with lettuce, topped with relish and chopped hazelnuts.