Start by cooking the potatoes: thoroughly wash the unpeeled potatoes and place them in a large pot filled with salted water. Boil for about 30 minutes until tender, then drain and let them cool until warm. Once warm to the touch (do not let them cool completely), peel the potatoes and place them on a cutting board.
Slice the warm peeled potatoes and then cut them into medium-sized cubes. Transfer the cubes to a large mixing bowl.
Wash and finely chop the parsley. Finely chop the anchovy fillets and capers as well.
In the bowl with the potatoes, add the torn fresh basil leaves, extra virgin olive oil, and the chopped anchovies and capers.
Add the chopped parsley, a pinch of freshly ground black pepper, and dried oregano.
Finally, drizzle with the white wine vinegar and toss gently with a spoon until evenly combined. Allow the potato salad to rest for at least 30 minutes at room temperature so the flavors can meld before serving.