Roll out both blocks of pastry to a thickness of ⅛ inch and cut out 18 discs, using a 4-inch cutter or saucer. Cover the discs with plastic wrap and chill while you prepare the filling.
Heat a saucepan over medium heat and add a little olive oil. Sweat the onion and garlic gently for about 5 minutes until soft but not colored. Add the cumin, cinnamon, and paprika and stir until aromatic.
Add the beef, season with salt and pepper, and cook for about 5 minutes until lightly browned. Mix in the olives, oregano, chile flakes, sugar, and hard-boiled eggs. Taste and adjust the seasoning as necessary. Leave to cool.
Once the beef has cooled, spoon about 1 tablespoon onto each pastry disc, leaving a ¼-inch border around the edge. Brush beaten egg around half the border, then fold the pastry over and press the edges together to seal and create a half-moon shape. Crimp the edges, removing any air pockets as you go.
Chill the empanadas for 20 minutes to firm up. Meanwhile, preheat the oven to 350ºF.
Place the empanadas on a baking sheet. Make a steam hole in the top of each one with a skewer, then brush with beaten egg. Bake in the preheated oven for 18–20 minutes until the pastry is golden brown.
Meanwhile, make the chimichurri. Place the parsley, garlic, and fresh oregano (if using) in a small food processor and roughly chop. Add the rest of the ingredients and process briefly to combine. Taste and season with salt and pepper. (If using dried oregano, add it at this stage.)
Once the empanadas are cooked, cool on a wire rack. Serve warm or at room temperature with the chimichurri on the side to spoon over or dip into.