For the potato brandy rings, peel the potatoes, boil and let cool.
In the meantime, bring water and milk to a boil. Add the butter and let it melt. When the butter is melted, add the flour all at once and stir vigorously with a wooden spoon.
It will be a bit crumbly at first, but after 3-4 minutes a ball of dough will form. Place this ball in a bowl and stir in the eggs, one at a time. Continue to stir for another 5 minutes until everything is nice and creamy. Then add salt and pepper.
Mash the cold potatoes (coarsely or very finely, depending on your taste). Grate in a little nutmeg and add 2 tablespoons of milk, stir and season with salt and pepper.
Preheat the oven to 190 °C convection oven. Now carefully mix the puree and choux pastry together with the dough scraper. Place in a piping bag with a large nozzle and pipe small rings about 8 cm in diameter onto a baking tray lined with baking paper.
Mix the egg yolk and 2 tablespoons of milk and brush the rings with it. Bake for 30 minutes on the middle shelf until golden brown.