Bring eggs to a boil in a small saucepan. Cover and remove from heat. Let stand 13 minutes. Drain and run eggs under cold water, then peel and cut in half.
Meanwhile, bring potatoes to a boil in well-salted water in a medium saucepan. Reduce heat and simmer until tender, about 8 minutes. Remove potatoes with a slotted spoon and return water to a boil. Blanch beans in batches until bright and just tender, 3 to 4 minutes, then transfer to an ice bath.
Whisk together mustard and vinegar in a small bowl. Gradually add oil, whisking to emulsify, and season with salt and pepper.
Arrange eggs, potatoes, beans, tuna, and olives on a platter and drizzle with vinaigrette before sprinkling with basil.
Look for pole-caught albacore tuna, ideally sourced from the United States, often labeled "chunk white." Skip cans not clearly marked as being troll- or pole-caught.