Cook the potatoes in boiling salted water until tender, about 30 minutes. Drain; cool. Peel the potatoes, cut into 1-inch pieces and place in the bowl. Drizzle the oil over the potatoes; toss to coat.
Add the cucumber, tomatoes, onion, olives, basil and capers to the bowl.
In a small bowl, whisk together the vinegar and oregano; drizzle onto the salad, and mix to combine.
Season the salad with salt and pepper. Garnish with eggs, and serve.