Blend the flour and 1/2 tsp salt in a food processor. With the motor running, add the egg yolks and the oil through the feed tube, then pour in the water in a slow, steady stream until the dough forms a ball around the blade. Transfer the dough to a floured surface and knead until smooth, about 2 minutes. Cover with a cotton cloth and let stand for 30 minutes.
Divide the dough into 12 equal pieces and shape them into balls. Let stand, covered with a cotton towel for 15 to 20 minutes.
Meanwhile, make the filling. Combine the lamb, sirloin, garlic,onions, and cilantro in a bowl. Season with salt and pepper.
On a floured surface with a floured rolling pin, roll out the dough into rounds, about 3 inches in diameter. Brush each one with melted butter, stack them on top of each other and let stand, covered with a towel, for about 15 to 20 minutes more. Roll out each round some more and then pull the sides of each until they are about 6 inches in diameter, taking care not to tear the dough.
Mix the ice water into the filling and divide the filling into 12 equal portions. Place a filling portion on one side of each round of dough. Fold the other half over the filling and press the edges together. Trim the edges even with a sharp knife and seal with the tines of a fork. (NOTE: I use a dough press used exclusively for this purpose. Makes Chebureki, pierogi, empanada, etc making so much easier!)
Heat the oil in a deep fryer to 375 degrees F.
Fry the Chebureki until deep golden brown, 3 to 4 minutes on each side. Drain on paper towels. Serve at once.