Peel and wash the potatoes; cut them in half lengthwise and place them in a pan that’s large enough to contain them all, one beside the other, in a single layer. Add the water and milk so it just covers them (if 1 glass of each isn’t enough, add a little more) and boil over a moderate heat until the potatoes are cooked. Mash them or put them through a food mill. Put the mashed potato into a large bowl, while it’s still hot add the butter (at room temperature), mix thoroughly, season with salt, pepper, nutmeg and lastly, one by one, add the yolks and one whole egg. Stir well, until you obtain a compact mixture with a smooth texture. Line a baking tray with greaseproof paper. Put the potato mixture into a piping bag and form rosettes (slightly larger than a walnut), a few centimetres apart, directly on the paper in the tray. Beat the remaining egg in a small bowl and then brush it over the potato rosettes. Bake them in a preheated oven, at 200 °C, until they turn golden (it will take about 25-30 minutes).