Rice Filling. Start making filling by bringing water to the boil. Add rice and simmer until water is absorbed in rice. Add milk, bring mixture to the boil and let it cook for a couple of minutes, stirring continually with a wooden spoon. Reduce heat to the minimum — or turn it off completely — cover pan with lid and let mixture simmer for about 30 - 40 minutes, stirring every now and then. Filling is ready, when it has thickened into a velvety, white porridge. Add a lump of butter, mix, cover pan with lid and set aside to cool. After cool, Mix egg(s) or yolk(s) in rice porridge and season with salt. Note: filling mustn't be too runny, it should hold its shape when spread on pie disks.
Potato Filling: Cook potatoes in water until tender. Reserve liquid. Puree potatoes through food mill and let cool a bit. Add eggs and enough cooking liquid and cream to get smooth mixture. Amount of liquid depends on the quality of potatoes — filling mustn't be too runny. Add a lump of butter and mix. Season with salt, cover and set aside to cool.
Prepare pasty dough: mix flour and salt, add oil and water little at a time and mix to get a non-sticky dough. Divide dough in 15 - 20 equal pieces and roll them into small balls. With a tapered rolling pin, roll out balls one at a time into very thin disks, about 1 mm thick and 10 - 15 cm in diameter. (You could also try and use a pasta machine for rolling.) Cover pie disks lightly with plastic wrap to prevent them from drying out.
Spread filling (either potato or rice) on centre of pie disks. Raise edges of pie disks towards the centre, pinching with your fingers to make an oval ridge - center will be open.
Place pasties on baking sheet covered with parchment paper and bake at 255 - 300°C for about 5 - 7 minutes or until pasties start to turn darkish brown. Meanwhile, heat about 150 ml whole milk in saucepan, add big lump of butter and let it melt. Dip hot pasties one at a time into hot milk-butter mixture and place them in large bowl. Cover bowl tightly with parchment paper and towel, and let pasties soften for about half an hour.
Warm pasties are traditionally served with egg and butter spread. Pasties may also be eaten topped with plain butter, cheese, ham or reindeer roast slices, gravlax, shrimps or whatever you happen to like! Pasties can be reheated in oven or toaster.
Egg & Butter Spread: Cook eggs in boiling water for 10 minutes. Rinse eggs with cold water and shell them. Using a fork, finely mash warm eggs together with the butter. Season with salt, if necessary. You can use an egg slicer to slice the eggs before mashing. Slice them first crosswise and then lengthwise.