Peel and chop potatoes in even chunks (keep fairly large, but even). New potatoes can be kept whole. Place in salted water which contains a tablespoon of lemon juice. This will keep the potatoes from falling apart. For this salad it is important to try to cook these perfectly so that they just fall off the blade of a knife. Ensure that they are neither hard nor crumbly, as they will continue to cook once drained.
Whilst the potatoes are boiling, finely chop your onions. Using either a mezzaluna or large sharp knife, begin to add the anchovies to your onions, and continue to chop so that both ingredients are incorporated. Continue in this fashion with the capers and the olives so that all four ingredients are incorporated. Finely chop your flat leaf parsley, and incorporate into the mix.
Drain the potatoes immediately once they are cooked, put them into a large bowl. It is very important that whilst they are piping hot to add the dressing at this stage. The potatoes will absorb the flavours of the dressing.
Immediately sprinkle the hot potatoes with sea salt, cracked pepper, and drizzle with olive oil. Add the onion, anchovy, caper, olive and parsley mix. Pour over the juice of the lemons, tasting for seasoning. If you need more oil, add oil, if potatoes need more lemon, add more lemon juice.
Toss through chunks of tuna, and taste again for seasoning.
Let salad sit so the flavours can mingle and serve at room temperature. Can be served as a meal or a side-dish.