Bring a large pot of salted water to a boil over high. Fill a bowl with ice water, and set it next to the stove. Add green beans to boiling water; cook, stirring occasionally, until beans are crisp-tender, 2 to 3 minutes. Remove green beans to ice bath using a slotted spoon, reserving pot and water. Cool beans 30 to 45 seconds. Drain ice and water; place beans in a large bowl, and set aside.
Reduce heat under pot to medium-high. Add potatoes; cook, uncovered, until fork-tender, 20 to 25 minutes. Drain and let potatoes stand until slightly cooled, about 15 minutes.
Meanwhile, whisk together sherry vinegar, lemon juice, salt, and black pepper in a medium bowl. Add olive oil in a thin, steady stream, whisking vigorously, until mixture is emulsified and creamy, 2 to 3 minutes. Set dressing aside.
Peel potatoes, and cut into ¾-inch pieces. Add to bowl with green beans. Add tomatoes, tuna, bell pepper, onion, and olives. Drizzle salad with olive oil dressing; gently toss to coat. Cover salad, and chill until flavors meld, about 2 hours. Serve topped with eggs and sprinkled with black pepper and parsley.
