Scrub the potatoes and place in a large pot and cover by two inches with cold water. Salt generously and bring to a boil. Reduce heat and simmer until potatoes are just cooked, 10 to 15 minutes. When you can pierce them easily with a fork, they’re done. Drain in a collander and set it in the top of the pot to let them cool slightly.

While the potatoes are cooking, whisk the olive oil, mustard and lemon juice together in a small bowl. As soon as the potatoes are cooled enough to handle (but only just—you want this dish warm), slice them into halves and place them in a large bowl. Whisk the dressing again to combine, drizzle it over the potatoes and stir gently with a wooden spoon to coat potatoes.

Add the capers, shallots and parsley to the bowl and stir gently to combine. Adjust seasonings with salt (if needed) and pepper. Serve immediately. When you do, note that the capers and bits of shallot will want to sink to the bottom of the bowl. Make sure to spoon some over each serving.