Start making the filling by bringing the water to the boil. Add the rice and simmer until the water is absorbed in rice. Add the milk, bring the mixture to the boil and let it cook for a couple of minutes, stirring continually with a wooden spoon.
Reduce the heat to the minimum — or turn it off completely — cover the pan with a lid and let the mixture simmer for about 30 - 40 minutes, stirring every now and then. The filling is ready, when it has thickened into a velvety, white porridge. Add a lump of butter, mix, cover the pan with lid and set aside to cool.
It would be best to prepare the porridge on the previous day and store it covered in refrigerator, so that it will thicken and not be too runny when used to fill the pasties.
Prepare the pasty dough: mix the flour and salt, add the oil and water little at a time and mix to get a firm, non-sticky dough. Divide the dough in 15 - 20 equal-size pieces and roll them into small balls. With a tapered rolling pin, roll out the flattened balls one at a time into very thin disks, about 1 mm thick and 10 - 15 cm in diameter. (You could also try to use a pasta machine for rolling.) Cover the pie disks lightly with plastic wrap to prevent them from drying out.
Mix the egg(s) or yolk(s) in the rice porridge and season with salt. Spread the porridge filling on the centre of the pie disks1. Note: the filling must not be too runny, it should hold its shape when spread on the pie disks. Raise the edges of the pie disks towards the centre, pinching the edges with your fingers.
Place the pasties on a baking sheet covered with parchment paper and bake at 255 - 300 °C for about 5 - 8 minutes, until brown specks start to appear. Meanwhile, heat about 150 ml whole milk in a saucepan, add a big lump of butter and let it melt. Submerge the piping hot pasties one at a time in the hot milk-butter mixture and place them in a large bowl, preferably in one layer. Cover the bowl tightly with parchment paper and a towel, and let the pasties soften for about half an hour.
Warm pasties are traditionally served with egg and butter spread (see picture on right). The pasties may also be eaten topped with plain butter, cheese, ham or reindeer roast slices, gravlax, shrimps or whatever you happen to like! The pasties can be reheated in oven or a toaster.