Place a baking sheet in the oven and preheat to 450˚. Toss the carrots with 1 tablespoon olive oil in a bowl; season with salt and pepper. Spread out on the hot pan and roast until tender and browned on the bottom, 25 to 30 minutes.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the green beans and cook until crisp-tender, 2 to 4 minutes. Remove with a slotted spoon to a paper towel–lined plate to cool. Carefully add the eggs to the pot of water; adjust the heat to maintain a gentle simmer and cook until the yolks are jammy, 7 minutes. Drain the eggs and run under cold water until cool enough to handle. Peel the eggs and cut each into 4 wedges.
While the eggs are cooking, make the dressing: Whisk the tahini, 1/4 cup water, 1 tablespoon olive oil and 1 tablespoon vinegar in a small bowl; season with salt and pepper. Thin with more water, if necessary.
Toss the lettuce in a large bowl with the remaining 1 tablespoon olive oil and 1 tablespoon vinegar; season with salt and pepper. Divide among plates. Top with the tuna, roasted carrots, green beans, radishes, olives and eggs. Drizzle with the tahini dressing and sprinkle with za'atar.