Whisk together the olive oil, vinegar, shallot, 1/2 teaspoon salt and a few grinds of pepper in a large bowl.
Cook the potatoes in the boiling water until tender, about 8 minutes. Transfer the potatoes to a colander with a slotted spoon and run under cold water to stop the cooking process. Add them to the bowl with the dressing. Cook the green beans in the boiling water until crisp-tender, 3 to 4 minutes. Transfer the beans to the colander with the slotted spoon and run under cold water. Add them to the bowl.
Add the pasta to the boiling water and cook according to the package directions. Drain and rinse under cold water to cool; add to the bowl.
Add the tuna, celery, olives, anchovies and tomatoes to the bowl and toss to combine. Season with salt and pepper. The pasta salad is best if served right away.
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