For the dough: Place the flour, cold water, oil and salt in a food processor and process until a smooth dough ball forms, about 5 minutes. Cover and set aside.
For the filling: Combine the beef, pork, onions and garlic in a bowl, then sprinkle with salt and pepper and mix well.
Bring a small pan of water to a boil. Add a tablespoon of the meat mixture and boil just until cooked through, about 3 minutes. Remove from the water and let cool before tasting. Adjust the seasoning of the meat mixture as needed with salt and pepper. Once adjusted, keep the filling in the refrigerator until ready to assemble.
Divide the dough into 2 equal portions and roll each portion out to 1/8-inch thick over a lightly floured surface, making sure its size is at least 2 inches bigger than the pelmeni mold. Place a layer of dough over the pelmeni mold and place a spoonful of filling over each hole. Lay another piece of dough on top and seal, pressing tightly.
Place the finished pelmeni on a floured board and let rest for 1 hour, uncovered.
Bring a large pot of salted water to a boil and gently place the pelmeni in the water. Cook until the pelmeni float, then cook an additional 4 to 5 minutes. Drain and place on a large platter.
To garnish: Stir the sour cream and vinegar together in a small bowl. Drizzle over the dumplings and garnish with the paprika and some hot sauce.