Cook the potatoes whole, with their skins on. When they are cooked and cooled, peel the skins off with a knife and cut them into small cubes.

In a heavy saucepan or top of a double boiler mix the sugar, flour, dry mustard, salt and turmeric. Stir together well. Whisk in milk, egg yolk and vinegar.

Cook the mixture over a saucepan of simmering water or in a double boiler, over medium heat, until the mixture is thick enough to coat the back of a spoon, about 10 minutes.

Stir in the butter. Let the mixture cool, stirring often. The dressing will keep thickening as it cools.

Pour the dressing over the potatoes and mix lightly until thoroughly combined.