Make the Dough:

1. Prepare the Dough: In a large bowl, combine the flour and salt. Add the cold butter pieces and, using your fingers or a pastry cutter, rub the butter into the flour until the mixture resembles coarse crumbs.
2. Add Wet Ingredients: Add the egg, vinegar (if using), and gradually add cold water, mixing until the dough just comes together. Add more water if necessary, but don’t overwork the dough. It should be smooth and slightly soft.
3. Chill the Dough: Shape the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes while you prepare the filling.

Prepare the Filling:

4. Cook the Vegetables: In a large pan, heat olive oil over medium heat. Add the chopped onion (and bell pepper, if using) and cook until softened, about 5-7 minutes. Add the garlic and cook for another 30 seconds until fragrant.
5. Add the Spices: Stir in the tomato paste, cumin, paprika, and turmeric (if using), and cook for 1-2 minutes, allowing the spices to bloom.
6. Add the Chicken: Add the shredded chicken to the pan, stirring to combine with the vegetables and spices. Pour in the chicken broth and let the mixture cook for 5 minutes, allowing the flavors to meld. Season with salt and pepper to taste.
7. Add Olives and Cilantro: Stir in the chopped olives and cilantro (if using). Remove from heat and let the filling cool slightly.

Assemble the Empanadas:

8. Preheat the Oven (if baking): Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper or a silicone baking mat.
9. Roll Out the Dough: Once the dough is chilled, roll it out on a lightly floured surface to about 1/8-inch thickness. Use a round cutter (about 4 inches in diameter) to cut out circles of dough.
10. Fill the Empanadas: Place a spoonful of the chicken mixture in the center of each dough circle, leaving a small border around the edges. Brush the edges with a little water, then fold the dough over to form a half-moon shape. Press the edges together to seal, crimping with a fork for a decorative finish.
11. Egg Wash (for baking): Brush the tops of the empanadas with the beaten egg to give them a golden finish when baked.

Bake or Fry the Empanadas:

To Bake: 12. Bake: Place the empanadas on the prepared baking sheet and bake for 25-30 minutes, or until golden brown and crispy. Remove from the oven and let cool slightly before serving.

To Fry: 13. Fry: Heat a few inches of vegetable oil in a deep pan over medium-high heat. Once hot (about 350°F or 175°C), carefully lower the empanadas into the oil, a few at a time, and fry for 3-4 minutes, or until golden and crispy. Remove and drain on paper towels.