Peel the potatoes, then boil in deep, salted water. Trum and rinse the leeks, discarding the dark outer leaves, and slice them thinly. Melt the butter in a shallow pan and cook the leeks in it over a low heat, stirring from time to time, until they are soft and melting; they should be ready in 20 minutes or so. If they colour they will turn bitter, so cover them with a lid or a piece of parchment paper.

Bring the milk to the boil in a small saucepan, then switch off the heat. When the potatoes are tender, drain them, put them back on the heat for a minute, covered with a lid or tea towel, to dry out, then mash them with a potato masher, pouring in the warm milk as you go. You are after a thick mash, not a sloppy one, so stop adding milk when the consistency is thick enough to make into patties. Stir in the leeks and season generously.

When the mixture is cool enough to roll, shape it into rough patties. Don't be tempted to make them perfectly smooth; they will be all the more interesting if they are a little rough.

Heat some oil in a shallow pan. When it is hot, slide in the patties, not too close together, and let them colour lightly on both sides. They will cook quite quickly, about three or four minutes on both sides. Lift the patties out with a spatula and drain briefly on paper towel.