Preheat the oven to 450 degrees F. Bring a large pot of salted water to boil. Prepare an ice bath. Line a sheet pan with a kitchen towel or paper towels.

To make the vinaigrette, whisk ¼ cup of olive oil, lemon juice, and mustard (optional) in a small bowl and season with salt and pepper; set aside.

Add green beans to boiling water and cook until tender-crisp, about 3 to 4 minutes. Remove from pot using a slotted spoon or strainer (don’t dump the water) and immediately plunge them into the ice bath to chill completely. Drain again and lay them out on prepared sheet pan to dry.

After removing the green beans, add the potatoes to the pot (add more water to cover, if needed). Return to a boil, reduce heat, and simmer until the potatoes are fork-tender, 15 to 20 minutes. Drain and set aside until just cool enough to handle. Cut potatoes into ½-inch slices, drizzle with 2 tablespoons of the vinaigrette, and toss while they’re still warm.

While potatoes cook, heat 2 tablespoons of olive oil in a small saucepan over medium-high heat. Add capers and cook, swirling pan occasionally, until capers burst and are crisp, about 7 minutes. With a slotted spoon, transfer capers to the lined sheet pan with the green beans. Reserve the oil.

Rub salmon all over with the caper oil and season with pepper. Place the salmon, skin side down, on a sheet pan and roast for 12 to 15 minutes, until fish is easily flaked with a fork.

When ready to assemble, use a fork to break salmon into large flakes, and cut hard-boiled eggs in half. Arrange the sliced potatoes, green beans, salmon, eggs, and olives on a platter or individual plates. Drizzle with half the dressing, top with fried capers and season with salt and pepper. Serve with remaining dressing on the side.