1Combine the dill, vinegar, mustard, salt, and a pinch of black pepper in a small bowl. Stir to combine, then whisk in the oil until thick and emulsified. Set aside.
2Put the whole potatoes in a large sauce pan and cover generously with cold water. Add a big pinch of salt and bring to the boil over high heat. Reduce the heat so the water’s at a steady simmer, and cook until the potatoes are cooked but not falling apart (check by piercing a potato with the tip of a small knife), about 25 minutes. Drain and spread the potatoes out in a single layer to cool until they’re easy to work with, about 10 minutes.
3Cut the warm potatoes in half lengthwise and place in a large bowl along with the cucumber slices and red onion. Add the dressing, stir to coat well, and serve immediately.