Boil the potatoes until just under-done. Let them dry in a colander then cut in half. Meanwhile, boil or steam the beans until al dente.
Heat the butter in a heavy frying pan. When bubbling, add the halved potatoes and saute until nicely coloured.
Use a slotted spoon to remove them from the pan and set aside.
Get the pan back to temperature and add the lardons. Fry for a couple of minutes, then add the livers (you want these to be ready at the same time, so if you prefer the livers well done, put them in earlier, if you prefer them pinker, you'll want to wait. It all depends on the size of your lardons and liver chnks - use your judgement!).
Once the livers are just browned, add the balsamic vinegar and continue to cook until the meat is cooked. Add a little more balsamic if it reduces too quickly. Season with freshly ground black pepper and sea salt.
Assemble everything into a bowl immediately before serving, pouring over the reduced balsamic jus as a dressing. Serve immediately, or the lettuce will start to wilt.