Put the potatoes in a medium saucepan and add water to cover. Bring to a boil, add a generous pinch of salt and simmer over medium heat until tender, 15 to 20 minutes. Drain and transfer them to a plate to cool slightly.
Meanwhile, whisk together the shallot, lemon zest and lemon juice in a large bowl; let stand for 5 minutes.
Using your fingers, lightly crush the potatoes and transfer to the large bowl. Add the olive oil and mix gently, then fold in the arugula, parsley, dill and chives. Season generously with salt and pepper. Serve right away.