Fill a medium bowl with ice water. Place the eggs in a small, deep saucepan, cover them with cold water by 1-inch. Bring to a boil over high heat, then immediately cover with a lid, remove from heat, and let stand for 12 minutes. Use a slotted spoon to transfer the eggs to the prepared ice-water bath until completely cool, about 10 minutes. Peel and quarter the eggs; set aside.
Prepare another bowl of ice water. Fill a small saucepan two-thirds of the way with water and bring it to a boil over high heat. Add 2 teaspoons salt and the green beans. Cook until the beans are bright green and tender-crisp, 2 to 3 minutes. Remove and strain the beans, then immediately plunge them into the ice water to stop the cooking. Once cool, rain and set the green beans aside on a towel to dry.
In a food processor or blender, combine the anchovies, garlic, parsley, Dijon mustard, lemon zest and juice, and two-thirds of the olive oil. Puree until well blended, 2 to 3 minutes. Add the mayonnaise, a few pinches of salt and a grind or two of pepper. Pulse a few times to incorporate into a creamy dressing. Set aside.
Hand-tear the lettuce into bite-size pieces (or leave the leaves whole for a dramatic fork-and-knife presentation). In a medium bowl, combine the lettuce with half of the remaining olive oil and a few pinches of salt and pepper, then toss to coat. Transfer the coated lettuce to a platter or divide them between 4 dinner plates. Using the same medium bowl, combine the reserved green beans, radishes, and tomatoes with the remaining 1 olive oil and a bit of salt and pepper. Scatter the tuna and its oil over the lettuce (or crumble into a tidy mound), add the eggs, radishes, tomatoes, olives, and green beans. Pour the dressing over everything, toss, and serve. You can also toss everything in a bowl and serve that way or compose the salad and serve the dressing on the side.