Bring 2 medium pots of salted water to a boil. Add the potatoes to 1 pot and blanch until tender, about 5 to 6 minutes. Drain in a colander, pat dry, and set aside. Add the green beans to the other pot and blanch until tender, 4 to 5 minutes. Drain in a colander, pat dry, and set aside.
Arrange the tuna on a cutting board and cut into 4 equal portions. Season the tuna steaks with 1/4 teaspoon salt and 1/4 teaspoon pepper, each. Heat the oil in a large skillet (or 2 medium skillets), over medium-high heat. When the oil is hot but not smoking, add the rosemary sprigs and tuna steaks and sear, about 30 seconds per side for medium-rare. Remove from the pan and dice the tuna into 1-inch pieces.
Tear the lettuce into bite-size pieces and combine with chopped fresh parsley and tarragon. Toss with enough of the Anchovy Dressing just to coat. Adjust seasonings with salt and pepper as needed. Toss the potatoes and green beans in 1/4 cup of the Anchovy Dressing. Arrange the lettuce along the side of 4 large plates (or 1 serving platter). Spoon the vegetables along the other side of the plate. Arrange the diced tuna over the lettuce. Arrange the tomatoes, olives, sliced red onions, and eggs on the other sides of the plates (or serving platter). Garnish with additional herbs if desired and serve immediately.
In a medium bowl, mash the anchovy, salt, pepper, and garlic into a paste with the back of a fork. Add the egg and whisk well to blend. Add the lemon juice and mustard, and whisk well. Add the oils in a steady stream, whisking constantly to form a thick emulsion. Add the shallots, capers and Worcestershire, whisk well, and adjust the seasoning, to taste. Cover and refrigerate until ready to use.