Peel and boil the potatoes until somewhat soft but still giving a little resistance when piercing through with a thin knife. Let cool. Dice the potatoes into 1-inch cubes (2.5 cm).
In a large bowl, combine all the other ingredients, add the potatoes, and season generously with salt and pepper. Taste if it needs more lemon juice or acidity or fresh herbs as well.
Refrigerate and let the salad sit for a few hours before serving to allow all the flavors to blend in. Serve room temperature with your favorite BBQ food or grilled foods.