This Is particularly good served with fish, such as fresh tuna burgers or deep-fried or grilled fish.
Bake or boil the potato until tender, then drain and leave until cool enough to handle. Mash to a purée and leave to cool completely.
Put the potato in a bowl and beat in the egg yolks. Whisk in the olive oil, drop by drop to begin with, then in a thin stream, as for making mayonnaise. It may be necessary to thin the aïoli with a little cold water; the consistency should be like mayonnaise.
Add the garlic and anchovies and stir all together. Season with salt and pepper.