To make the lemon-shallot vinaigrette, in a small bowl, whisk together the olive oil, lemon juice, shallot, garlic, Dijon mustard, thyme, and salt and pepper to taste (I like ½ teaspoon salt and ¼ teaspoon pepper). Let the flavors blend while preparing the salad.
Set out a large bowl of ice water for chilling the potatoes and the green beans. In a medium saucepan, add potatoes, 1 teaspoon salt, and cold water to cover by 1 inch.
Bring to a boil, reduce heat to medium, and cook uncovered until potatoes are tender and can easily be pierced by a knife, about 10 to 15 minutes. Drain well and immediately plunge into ice water to stop the cooking.
To the same saucepan, bring 1 quart water and 1 teaspoon salt to boil. Add the green beans and boil until tender-crisp, but still bright green, about 3 minutes. Drain well and add to the ice water with the potatoes to stop the cooking. Drain the potatoes and green beans well and cut the potatoes into quarters.
In a medium bowl, add the field greens, drizzle with 2 tablespoons vinaigrette, and toss to coat. Arrange on the bottom of a large platter.
Arrange the quartered potatoes, green beans, tomatoes, and olives in piles around the sides of the platter with the tuna in the middle. Drizzle the potatoes, green beans, and tomatoes with vinaigrette, serving the remaining vinaigrette on the side.
Season the hard-boiled eggs, potatoes, and tomatoes generously with salt and pepper and garnish the platter with fresh thyme.