
Butter-Basted Salmon with Hazelnut Relish
['1/2 cup blanched hazelnuts', '1 garlic clove, chopped', '1 cup (packed) fresh cilantro leaves with tender stems', '1/2 cup (packed) fresh flat-leaf parsley leaves with tender stems', '1 tablespoon capers', '1 teaspoon finely grated lemon zest', '1/2 cup olive oil', 'Kosher salt', '1 tablespoon vegetable oil', '4 6-ounce 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. Let cool.
Pulse garlic, cilantro, parsley, capers, lemon zest, and 1/4 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.
Do ahead: Relish can be made 6 hours ahead. Cover and chill.
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