Make the chimichurri: In a bowl, combine parsley, oregano, garlic, olive oil, red wine vinegar, red pepper flakes, salt, and pepper. Adjust acidity and salt to taste.
Set aside to let the flavors meld while you prepare the filling.
Sauté the aromatics: Heat olive oil in a skillet over medium heat. Add onion and cook until soft and translucent, about 4–5 minutes. Stir in garlic and cook 30 seconds more.
Cook the protein: Add ground beef to the skillet.
Break it up with a spoon and cook until browned and no longer pink. Drain excess fat if needed.
Season and simmer: Add cumin, smoked paprika, oregano, red pepper flakes, salt, and black pepper. Stir in tomato paste and broth.
Simmer 3–4 minutes until the mixture thickens and looks glossy. Taste and adjust seasoning.
Finish the filling: Stir in olives and chopped hard-boiled eggs if using. Let the filling cool to room temperature; this helps the dough seal well.
Assemble the empanadas: Lay out empanada discs.
Place 2–3 tablespoons of filling in the center of each. Brush the edges with beaten egg, fold into a half-moon, and press to seal. Crimp with a fork or pinch to make a decorative repulgue.
Preheat the air fryer: Set to 375°F (190°C) for 3 minutes.
Lightly spray the basket with oil.
Cook in batches: Arrange empanadas in a single layer with space between them. Lightly brush or spray tops with oil. Air fry for 10–13 minutes, flipping halfway, until golden and crisp.
Time may vary by model and dough thickness.
Serve: Let cool 2–3 minutes. Serve warm with chimichurri on the side or drizzled over the top.