In a bowl, mix together the rye flour, wheat flour and salt together until well-combined. Add the water gradually, mixing with a spatula at first, then knead with your hands until you get a smooth dough.
Now it's time to form the individual pies.
Take out a small portion from the dough and spread them out thinly on a floured surface using a rolling pin. You want to get an oval shape of about the same size as your palm. Remember that the thinner the dough the crispier it will be once it's baked!
Take about a spoonful or two (depending on how much filling you want the pastries to have) of the rice pudding filling, place it in the middle of the dough crust and spread it out in an even layer, but don't get too close to the edges!
Grab the two longer sides of the oval and fold them inward. Using your thumb and index finger, pinch at the folded edges from the center to the ends, to form the pleats that make up the signature shape of the Karelian pies.
Place the finished pies carefully on a tray lined with parchment paper.
Preheat the oven to 260° C/ 500° F.
Place them in the oven and bake for about 15 minutes or until the porridge filling turns a nice golden brown color.
While the pies are baking, prepare the egg and butter spread.