Divide one of the chilled discs of dough in half and place one half back in the refrigerator. Roll the remaining half on a lightly floured surface into a 9x12 inch rectangle. It should be about 1/8 inch thick.
Use a 4 inch round cookie cutter or glass to cut out 6 circles. If not immediately ready to use, place the circles on a parchment lined baking sheet in single layers separated by more parchment. Refrigerate until ready to assemble.
Put a circle of dough in the palm of your hand and place a heaping tablespoon of chorizo filling in the center. Fold the dough over to enclose the filling and form a half moon. Lightly brush the edge with water before using a fork to press the edges to seal. Repeat with remaining dough and filling.
Pour the 2 cups oil into medium pot or deep fryer. It should be deep enough to submerge the empanaditas. Heat to 375˚F.
Fry the empanaditas in batches, being careful not to overcrowd, until golden on each side, 3-4 minutes total. Use a slotted spoon to transfer to a towel lined plate. Repeat with remaining empanaditas. Serve warm.