Step 1: Make the Dough

1. In a large mixing bowl, combine the flour, salt, and sugar.
2. Add the cold butter cubes and use your fingers or a pastry cutter to incorporate the butter into the flour until the mixture resembles coarse crumbs.
3. In a separate small bowl, whisk together the egg, ice-cold water, and vinegar.
4. Slowly pour the wet ingredients into the flour mixture, stirring until the dough comes together.
5. Knead the dough lightly until it forms a smooth ball. Wrap it in plastic wrap and refrigerate for at least 30 minutes. This helps relax the gluten and makes the dough easier to roll out.

Step 2: Prepare the Beef and Cheese Filling

1. In a large skillet over medium heat, cook the ground beef until browned. Drain excess fat if necessary.
2. Add the chopped onion and garlic, cooking until softened, about 3 minutes.
3. Stir in the salt, black pepper, cumin, smoked paprika, and chili powder.
4. Add the tomato sauce, mixing well to combine. Let the mixture simmer for 5 minutes, allowing the flavors to meld.
5. Remove from heat and let the filling cool slightly.
6. Stir in the cheddar and mozzarella cheese, mixing until melted and combined.
7. Finally, mix in the chopped parsley or cilantro. Set aside.

Step 3: Assemble the Empanadas

1. Roll out the chilled dough on a lightly floured surface to about ⅛ inch thick.
2. Use a 3-4 inch round cutter (or a small bowl) to cut out dough circles.
3. Place about 1 ½ tablespoons of filling in the center of each circle.
4. Lightly wet the edges of the dough with water, then fold the dough over to form a half-moon shape.
5. Press the edges together and seal by crimping with a fork or twisting the edges for a decorative seal.

Step 4: Bake or Fry the Empanadas

Baking Method

1. Preheat your oven to 375°F (190°C).
2. Place the assembled empanadas on a lined baking sheet.
3. In a small bowl, whisk the egg and milk (or water) to make an egg wash. Brush the tops of the empanadas with the egg wash for a golden finish.
4. Bake for 20-25 minutes, or until golden brown.

Frying Method

1. In a large skillet or deep fryer, heat vegetable oil to 350°F (175°C).
2. Fry the empanadas in batches, cooking for about 2-3 minutes per side, or until golden brown and crispy.
3. Drain on a paper towel-lined plate to remove excess oil.