Begin by making the munavoi (egg butter) so it has time to cool in the fridge. Peel the hard-boiled eggs and, using either a fork or potato masher, make a thick egg paste in a bowl, mixing the butter in carefully. Add salt, cover with clingfilm and cool in fridge for at least one hour.
To prepare the rice filling, place rice in a saucepan, add water and cook until the water is completely absorbed - keep an eye on it so the bottom does not burn, or you'll have to start again. Add the milk and, stirring constantly, bring to boil. Simmer for at least half an hour until the rice is well-cooked but not too soft. Season with salt and butter, as you like it, and allow to cool.
To make the dough, stir both white and rye flour together, add salt then knead into a solid dough. The key to making good dough is to use your fingertips correctly. Once the dough is the right consistency, put onto a well-floured cutting board. Using a knife or a scraper, cut the dough into 20 uniform pieces - they should all be the same size once baked for best visual appeal. Roll each piece into a small ball and flatten.
Once they are flat, roll each piece as thinly as possible, then fill with a dollop of rice porridge that has cooled. With the filling in the middle, use your fingertips to pinch around the crust so the rice does not leak from the “boat”.
Line a baking tray with greaseproof paper and place the pies on top. Bake at 275 – 300C or as hot as your oven will go for 10 – 15 minutes, until golden brown. After they are taken from the oven, brush them with melted butter then put on greaseproof paper. To ensure they are soft, cover with a tea towel.
Finally, add the egg butter on top, split nicely into 20 portions. Make sure you fill an oval in the middle so the golden brown crust is still visible.