Bring a large saucepan of water to the boil. Cook the potatoes for 20 minutes, or until tender.
Add the eggs for the last 10 minutes. Remove the potatoes and eggs, and allow to cool.
Peel the potatoes, then cut into 2-3cm / 3/4-1 1/4 inch cubes. Peel and chop the eggs. Place the
potatoes in a large bowl with the dill, eggs and shallots. Toss to combine, then season.
Process the egg yolk, lemon juice, mustard and a pinch of salt in a food processor. With the
motor running, gradually add the olive oil a few drops at a time. When about half the oil has been
added, pour in the remaining oil in a steady stream until it has all been incorporated. Use a large
metal spoon to gently combine the potato and mayonnaise, then serve.