Boil the potatoes whole in a large pot of water. Once tender (about 30 minutes), drain and set aside to cool.
Whizz all the remaining ingredients together in a food processor or with a hand blitzer (we call it the zigzigger).
Once the potatoes are cool enough to handle, break them apart gently with your hands into bite-sized pieces. This will make them more receptive to the dressing.
Put the potatoes in a large bowl and season generously with salt and white pepper. Pour the dressing over the waiting potatoes and stir together gently-gently with two wooden spoons.
Garnish with more dill leaves.