Put the potatoes into a pan with plenty of salted water and a bay leaf. Bring to the boil and cook until the potatoes are nice and soft. Gently drain, then cut the potatoes in half.
Put the eggs into a pan of boiling water and cook for 7 minutes, then remove them to a bowl of cold water.
Put 50ml of olive oil into a pan on a medium heat. Add the potatoes and cook until golden brown and caramelized. Add the shallots and cook gently, then add the ham for a couple of minutes – you don’t want it to crisp, just to lose its saltiness slightly. Stir in the tarragon.
Put the potatoes on a plate. Cut the boiled eggs into quarters and dot over the potatoes, then finish with the remaining olive oil, salt and pepper.