Make the Creamy Parmesan Dressing and set aside.

Bring 2 medium pots of salted water to a boil. Add the potatoes to 1 pot and blanch until just tender, about 3 1/2 minutes. Drain in a colander.

Add the green beans to the other pot and blanch until tender, 4 minutes. Drain in a colander.

Heat 1/4 cup of the oil in a large skillet over medium-high heat. Add the drained potatoes, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper, and cook, shaking the pan occasionally, until golden brown on both sides, 8 minutes. Add the remaining tablespoon of oil, garlic, and drained green beans. Stir to combine and cook for 1 minute. Add the tomatoes and olives and cook until the tomatoes are warmed through, stirring occasionally, 2 minutes. Remove from the heat. Add the mayonnaise, lemon juice, minced onion, hard-boiled egg, capers, parsley, and tarragon and stir to combine. Taste and adjust seasoning, if necessary.

Combine the lettuce with the Creamy Parmesan Dressing and toss to coat. Arrange 3 or 4 leaves along the side of 6 large plates. Spoon the vegetables along the other side of the plate. Let sit while cooking the tuna.

Season each tuna portion with 1/2 teaspoon of the remaining salt, and 1/4 teaspoon of the remaining pepper.

Heat the remaining 1/4 cup of oil in 1 large skillet or 2 medium skillets, over medium-high heat. Add the tuna and sear, about 15 seconds per side. Remove from the pan and cut each crosswise into 4 equal pieces. Arrange the tuna slices down the middle of each plate, and serve.

Bring a small saucepan of water to a boil. Add the egg and cook for 30 seconds until coddled.

In a small bowl, combine the salt, pepper, garlic, and anchovies. Mash the anchovies with the back of a fork and mix into the other ingredients. Add the egg and whisk well to combine. Add the cheese, lemon juice, and mustard, and whisk well. Add the olive oil in a steady stream, whisking constantly. Add the Worcestershire and pepper sauces, and whisk well. Taste and adjust seasoning, if necessary.