Steam the potatoes in 1/2 inch of water until tender, 16 to 18 minutes; drain.
Meanwhile, heat 1 tablespoon of the oil in a large nonstick skillet over medium high heat. Season the salmon with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook until opaque throughout, 3 to 4 minutes per side. Break into large chunks.
Using the flat side of a chef's knife, mash the anchovies and garlic into a paste on a cutting board. Combine with the lemon juice and the remaining 4 tablespoons of oil in a small bowl. Season with 1/4 teaspoon each salt and pepper. Stir in the dill.
Toss the arugula and potatoes with half the dressing. Divide the salad among 4 plates and top with the salmon. Drizzle with the remaining dressing.
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