Method:

1. First, make the dough: In the bowl of a food processor, combine the flour, egg, salt, and ½ cup water. Pulse until the mixture forms a ball of dough, then turn it out onto a lightly floured surface and knead until the dough is smooth and elastic, 4-5 minutes. Lightly oil a large bowl, transfer the dough to the bowl and cover with plastic wrap while you prepare the filling. 

2. In a medium bowl, combine the ground beef and pork, stock, onion cilantro, butter, garlic, chili, thyme, coriander, caraway, cumin, and ½ teaspoon kosher salt. Use a fork or your hands to mix the filling until thoroughly combined, then set aside. 

3. Divide the dough roughly into thirds and keep ⅔ of the dough covered while you roll out the first piece. Sprinkle your work surface lightly with flour then use a rolling pin to roll one piece of dough out to a thickness of about ¼-inch inch. Use a thin glass or circular cookie cutter 2½ inches in diameter to punch out as many circles as possible. Peel off the scraps of excess dough, make it into a ball, and add it to the remaining dough. Roll each circle out into a large, thin circle of about 4 inches in diameter. Place a packed tablespoon of filling into the center of one circle and begin pleating the edges together, gathering the dough at the top like a cloth pouch to trap the filling in the centre. When you have pleated all the way around, pinch the top knot together firmly and give it a little twist to make sure the khinkali is well sealed. Set the finished khinkali on a lightly floured baking sheet or platter. Continue making dumplings with the remaining dough and filling.