Step 1: Heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes.
Step 2: Add the ground pork and beef to the skillet. Break it up with a spoon and cook until fully browned, stirring occasionally. Drain any excess grease.
Step 3: Stir in the shredded cabbage. Cook, stirring frequently, until the cabbage has wilted significantly and softened, about 10-15 minutes. It should lose most of its volume.
Step 4: Add the cooked rice, tomato paste, paprika, salt, and black pepper to the mixture. Stir well to combine all ingredients. Taste and adjust seasoning as needed. Remove from heat and let the filling cool completely. This is crucial before assembling the dumplings.
Step 5: In a large mixing bowl, combine the all-purpose flour and salt. Gradually add the warm water, mixing with a wooden spoon or your hands until a shaggy dough forms.
Step 6: Transfer the dough to a lightly floured surface and knead for 5-7 minutes, until it's smooth and elastic. It should be soft but not sticky. Cover the dough with a clean kitchen towel and let it rest for at least 30 minutes. This resting period helps the gluten relax, making the dough easier to roll and more tender.
Step 7: Divide the rested dough into 3-4 equal portions. Keep the portions you’re not working with covered to prevent them from drying out.
Step 8: On a lightly floured surface, roll out one portion of dough into a thin circle, about 1/8 inch thick. Using a round cookie cutter (about 3-4 inches in diameter) or the rim of a glass, cut out circles of dough. Gather the scraps, knead lightly, and re-roll.
Step 9: Place about 1-2 tablespoons of the cooled filling in the center of each dough circle. Fold the dough over the filling to form a half-moon shape. Pinch the edges firmly to seal, ensuring no filling escapes. You can crimp the edges with a fork for extra security and a decorative touch. Repeat with the remaining dough and filling.
Step 10: Bring a large pot of salted water to a rolling boil. Carefully drop the assembled dumplings into the boiling water, making sure not to overcrowd the pot. Cook in batches if necessary.
Step 11: Once the dumplings float to the surface, cook for an additional 3-5 minutes. They should be tender and cooked through.
Step 12: Using a slotted spoon, remove the cooked dumplings from the water and drain well.
Step 13: Serve the hot dumplings immediately. They are traditionally enjoyed with a dollop of sour cream or a sprinkle of fresh dill. A touch of melted butter can also elevate the experience.