Make the dough. Dissolve the yeast and sugar in the warm milk and water. Add the melted butter, egg and salt. Mix in half of the flour, then gradually add the rest, kneading until you have a smooth, elastic dough. Cover and let rise in a warm place for about an hour, until doubled in size.
Prepare the filling. Cook the rice according to package instructions and let it cool. Sauté the ground beef and onion in a skillet until the meat is browned. Season with salt, white pepper and caraway or allspice. Stir in the cooled rice and, if using, chopped hard‑boiled eggs. Allow the mixture to cool.
Shape the pies. Punch down the dough and divide it into 8–10 balls. Roll each ball into a circle about 15 cm in diameter. Place 2–3 tablespoons of filling in the center, leaving the edges clean. Brush the edges with water, fold the circle in half and pinch the seam firmly to seal.
Fry. Heat oil in a deep pot to 170–175 °C (340-350 °F). Fry the pies two at a time, turning once, until they are deep golden brown. Remove with a slotted spoon and drain on paper towels.
Serve. Enjoy the pies hot. Split them lengthwise and add mustard, ketchup and cucumber relish. For atomi and vety, slide in a slice of ham and/or a boiled egg; for a heartier meal, add a hot dog.
