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Gently rub salmon fillets with 2 teaspoons oil, 1/3 teaspoon sea salt, and a good grind of pepper. Set aside while you make relish.
Add ⅓ cup olive oil to large sauté pan over high heat. Add celery and almonds and fry 4 to 5 minutes, stirring frequently, until nuts begin to brown and smell nutty. Turn off heat and stir in olives, parsley, lemon zest, and juice. Season with sea salt and pepper, to taste; set aside.
In large skillet, heat 1 tablespoon oil over medium-high heat until it shimmers. Add salmon fillets skin-side down and cook 3 minutes, until skin is crisp. Reduce heat to medium, flip fillets and cook another 2-3 minutes, until salmon is just cooked through. Serve salmon with warm celery olive relish spooned on top.