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Preheat the oven to 425°F. In a large saucepan over high heat, bring the lentils and broth to a boil. Reduce the heat, add the carrot, celery, shallot, herbes de Provence, and 3/4 teaspoon salt and cook, covered, until tender, 25 to 30 minutes, adding more stock or water if the lentils are dry before done. Remove from the heat, drain any liquid, and keep warm.
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Meanwhile, line a rimmed baking sheet with parchment paper. Rub the salmon fillets with 1 tablespoon of the olive oil, season generously with salt and pepper, place on the prepared baking sheet, and roast until just cooked and firm yet springy to the touch, 8 to 10 minutes.
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Stir 2 tablespoons of the olive oil and the vinegar into the lentils. Season to taste with salt. Divide the lentils among 4 plates and top each with a salmon fillet
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In a bowl, toss the arugula and drizzle with the remaining 1 tablespoon olive oil, a squeeze of lemon juice, and a pinch of salt and pepper. Divide atop each salmon fillet and serve immediately