In a large mixing bowl, combine the flour and salt. Add cubed butter and mix until the mixture resembles coarse crumbs.
Beat one egg and add it to the mixture. Gradually add cold water, mixing until a dough forms. Knead gently, wrap in plastic wrap, and refrigerate for at least 30 minutes.
In a frying pan, heat olive oil over medium heat. Sauté onions until translucent. Add garlic, cumin, paprika, and black pepper, and cook for an additional minute.
Stir in shredded chicken, and cook for 2-3 minutes until heated through. Remove from heat and allow to cool.
Preheat the oven to 375°F (190°C) if you plan to bake the empanadas.
On a floured surface, roll out the dough to about ⅛ inch thickness. Use a cookie cutter or glass to cut out circles about 4-5 inches in diameter.
Place about 2 tablespoons of the chicken mixture in the center of each circle. Fold the dough over to form a half-moon shape and crimp the edges with a fork to seal.
If baking, place the empanadas on a parchment-lined baking sheet. Beat the remaining egg and brush it over the tops of each empanada. Bake for 20-25 minutes, or until golden brown.
If frying, heat oil in a deep pan to 350°F (175°C). Fry the empanadas in batches until golden, about 3-4 minutes per side. Drain on paper towels.