01 - Preheat the oven to 400°F and line a baking sheet with parchment paper.
02 - Heat olive oil in a skillet over medium heat. Add finely chopped onion and cook until softened, approximately 3 minutes, then add minced garlic and cook for 1 additional minute.
03 - Add ground beef to the skillet and cook, breaking it apart, until browned and cooked through, about 6 minutes. Drain excess fat if necessary.
04 - Stir in ground cumin, smoked paprika, chili powder, salt, and black pepper. Add tomato paste and water, cook for 2 minutes until mixture is combined and slightly thickened.
05 - Remove skillet from heat. Fold in chopped green olives if using, shredded cheddar, and shredded mozzarella cheese. Allow filling to cool slightly.
06 - On a lightly floured surface, roll out pastry sheets and cut 12 circles approximately 4 inches in diameter.
07 - Place one heaping tablespoon of filling in the center of each pastry circle. Fold over to form a half-moon shape and press edges to seal. Crimp edges firmly with a fork.
08 - Arrange empanadas on the lined baking sheet and brush the tops with beaten egg.
09 - Bake in the preheated oven for 20 to 25 minutes, or until pastry is golden and puffed.
10 - Allow empanadas to cool slightly before serving.