In a large saucepan, add the potatoes and cold water to cover. Bring to a boil, add salt and cook the potatoes until just tender, 12 to 15 minutes. Drain and return to the saucepan.
Meanwhile, in a small bowl, ladle potato cooking water over the sun-dried tomatoes. Let soak for 10 minutes; drain and thinly slice.
Preheat a grill or grill pan to medium-high. Drizzle EVOO over the tuna, sprinkle with the rosemary and lemon peel and season with salt and pepper. In a large bowl, whisk together the 1/3 cup EVOO, lemon juice, anchovy paste and garlic. Toss with the potatoes, sun-dried tomatoes, red onion, celery, olives, capers and parsley.
Grill the tuna for 3 minutes on each side for medium-rare. Serve with the potato salad.