In a large bowl, whisk together the flour and salt. Add the chilled, cubed butter and use a pastry cutter or your fingers to blend until the mixture resembles coarse crumbs.
In a small bowl, whisk together the egg, cold water, and vinegar. Pour this mixture into the flour mixture and stir until the dough comes together.
Turn the dough onto a floured surface and knead gently until smooth. Wrap in plastic wrap and refrigerate for at least 30 minutes.
Step 2: Prepare the Filling
In a large skillet, heat the olive oil over medium heat. Add the finely chopped onion and cook until softened, about 3 minutes.
Add the ground beef to the skillet, breaking it up with a spoon, and cook until browned, about 5-7 minutes.
Stir in the minced garlic and diced bell pepper, cooking for another 2-3 minutes.
Add the tomato sauce, ground cumin, paprika, salt, and black pepper. Stir to combine and let the mixture simmer for 5 minutes.
Remove from heat and stir in the sliced olives and chopped hard-boiled egg, if using. Allow the filling to cool slightly.
Step 3: Assemble the Empanadas
Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
On a floured surface, roll out the dough to about 1/8-inch thickness. Use a round cutter (about 4-5 inches in diameter) to cut out circles of dough.
Place a tablespoon of filling in the center of each dough circle. Fold the dough over the filling to create a half-moon shape and press the edges together to seal. Crimp the edges with a fork for a decorative touch.
Place the assembled empanadas on the prepared baking sheet. Brush the tops with the beaten egg.
Step 4: Bake the Empanadas
Bake in the preheated oven for 20-25 minutes, or until golden brown.
Step 5: Serve
Allow the empanadas to cool slightly before serving. Enjoy them warm or at room temperature.
