Step 1

Preheat oven to 400°F. Bring a large pot of generously salted water to a boil over high. Add potatoes; cook, until almost tender, about 10 minutes. Add green beans; cook until potatoes are tender and green beans are tender-crisp, about 3 minutes. Using tongs or a slotted spoon, transfer potatoes and green beans to a bowl filled with ice water, reserving boiling water in pot.

Step 2

Using a slotted spoon, carefully lower eggs into boiling water; cook until whites are set and yolks are jammy, 7 1/2 minutes. Transfer eggs to bowl of ice water. Let potatoes, green beans, and eggs stand in ice water until cooled, about 5 minutes. Drain. Halve potatoes, and peel and quarter eggs.

Step 3

While potatoes, green beans, and eggs cook and cool, whisk together mustard, lemon zest, and 1/2 teaspoon each of the salt and pepper in a medium bowl. While whisking, gradually add 6 tablespoons of the oil, continuing to whisk until emulsified. Measure 2 tablespoons mixture into a separate small bowl for spreading on salmon, and set aside. Whisk lemon juice, shallot, and honey into remaining mustard mixture in medium bowl until combined; set dressing aside.

Step 4

Drizzle remaining 2 tablespoons oil evenly onto a baking sheet. Place salmon, skin side down, on oiled baking sheet, and sprinkle evenly with remaining 1/2 teaspoon each salt and pepper. Spread reserved 2 tablespoons mustard mixture evenly over salmon. Bake in preheated oven until just cooked through, about 12 minutes. Remove from oven, and let cool 5 minutes.

Step 5

Toss together lettuces and 3 tablespoons of the mustard-lemon juice dressing in a large bowl until lightly coated. Arrange on a platter, or divide evenly among 4 plates. Flake salmon into large pieces, and arrange evenly on lettuces. Top evenly with potatoes, green beans, eggs, and olives. Drape anchovy fillets evenly over salmon and vegetables. Drizzle evenly with remaining dressing, scatter with parsley, and serve.