1. Bring the rice to the boil with 700 ml milk and a pinch of salt, then simmer over low heat, stirring often, for 40-45 minutes into a thick porridge and leave to cool.
2. Knead the rye flour with the water and 1 teaspoon of salt into a firm, non-sticky dough, divide it into 16 equal balls and roll each one out on a floured surface into a thin oval of about 15 cm.
3. Spread 1-1.5 tablespoons of porridge in the middle of each oval, fold the edges 1-1.5 cm over the filling all the way round and pinch them closely with your fingers so they look ruffled, leaving the centre open.
4. Place on a baking tray lined with baking paper and bake in an oven preheated to 275 °C (or its maximum) for 10-15 minutes until the edges are spotted brown.
5. Meanwhile, heat 30 g of the butter with the remaining 200 ml milk and brush the pies straight away as they come out; cover them with a tea towel and let them rest to soften.
6. Hard-boil the eggs for 10 minutes, peel them, mash them with a fork with the remaining soft butter, season with salt and spread on top of the warm pies.
Tip: Karjalanpiirakka are the symbol of Karelia in eastern Finland and today a breakfast all over the country: you'll find them in every bakery and café. The thin rye dough seems tricky at first, but after the 4th or 5th pie the pinching comes naturally. The hot milk and butter wash and resting under a tea towel make the edges soft - skip it and they stay hard.
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