Wash potatoes thoroughly under cold running water. Place whole into a large pot, cover with cold water, and add a generous pinch of salt.

Bring to a boil over medium-high heat, then reduce to a steady simmer. Cook for 15 to 20 minutes until fork-tender but still holding their shape. Start checking at 15 minutes to avoid overcooking.

While potatoes cook, whisk together olive oil, lemon juice, sumac, salt, and black pepper in a small bowl until fully combined. Set aside.

Drain the potatoes and let cool for about 10 minutes until safe to handle. Peel if desired and cut into roughly 1-inch bite-sized cubes.

In a large mixing bowl, combine the warm potato cubes, parsley, red onion, cucumber, tomatoes, olives, and feta. Pour the dressing over the top and gently fold to coat without mashing the potatoes. Taste and adjust seasoning. Serve at room temperature or refrigerate for at least 1 hour before serving for best flavor.