For the filling: Heat the oil in a large skillet over medium heat. Add the potato. Cook and toss until golden on the edges, about 3 minutes. Add the onion along with a pinch of salt and cook until just softened, 3 to 4 minutes. Add the ham and garlic and cook until sizzling, about 1 minute. Add the beef and cook, breaking up into small crumbles with a wooden spoon, until browned, 2 to 3 minutes. Season with the abodo.
Add the red wine and simmer until reduced, about 1 minute. Add the tomato puree and 1/2 cup water. Simmer until the sauce is thick and flavorful, 8 to 10 minutes. Stir in the olives and capers and transfer to a bowl to cool.
For the chipotle chimichurri: Combine the parsley, garlic, scallions, vinegar and chipotle in a blender. Process to make a chunky paste. With the blender running, add the oil in a slow, steady stream to make a smooth, thick sauce. Season with salt. Transfer to a bowl and refrigerate while you form the empanadas.
For the empanadas: Unroll the pie dough. If there are any cracks in the dough, use a rolling pin to gently roll the dough back together. Use a 4-inch round cutter to cut as many circles as you can; you should get 10 to 12 rounds depending on the size of your pie crust. Repeat with the second pie crust. Beat the egg in a bowl with a fork. Add about a tablespoon of filling to each circle and brush the edges with egg wash. Form into half-moons and press the edges well to seal. Pleat the edges or crimp with a fork. Put the empanadas on a parchment-lined baking sheet. Repeat with the remaining dough and filling. Refrigerate the empanadas for 15 minutes to firm up slightly.
Heat 2 inches of vegetable oil in a large Dutch oven until a deep-fry thermometer reaches 365 degrees F. Line a baking sheet with a wire rack. Fry the empanadas in 2 batches until crisp and deep golden, 4 to 5 minutes per batch, letting the oil return to 365 degrees F between batches. Drain on the wire rack. Serve hot or warm with the chipotle chimichurri for dipping.