Cut any particularly large potatoes in half, leaving the smaller potatoes whole. Boil in a large pan of water (or vegetable stock, for extra flavour) until tender.
Meanwhile, melt half of the butter in a large frying pan, along with the olive oil. Add the garlic and cook over a medium-low heat for a couple of minutes, until fragrant.
Remove any thick, tough-looking stems from the samphire, and add it to the pan with the garlic. Sauté for 5 more minutes.
When the potatoes are cooked, drain them and add them to the pan, along with the remaining tablespoon of butter and plenty of black pepper. Mix to combine, and allow the butter to melt.
Add the fresh parsley just before serving