Cook the potatoes with skins on in lightly salted water until they are just done, tender but firm enough to slice, 20 to 25 minutes. Let cool slightly, then peel and dice.

Combine the warm potatoes, peppers and olives in a salad bowl. Break the tuna up with your fingers as you add it to the salad. Set aside.

Combine the oil, vinegar, cumin, paprika, black pepper and salt in a small bowl, whisking until the dressing is combined and thickened. Pour this over the salad ingredients and toss gently until all the ingredients are evenly dressed.

Serve on a chilled platter or plates garnished with the parsley.