Make the Dough:

Mix the flour and salt in a large bowl. Work the butter into the flour with your fingers until the mixture resembles coarse crumbs.
Beat the egg with the ice water and mix into the flour mixture until the dough comes together. If necessary, add more water one tablespoon at a time. Wrap in plastic and chill for at least 30 minutes.

Prepare the Filling:

Heat the olive oil in a pan over medium heat. Add the onion and garlic and cook until soft.
Increase the heat and add the ground beef, cooking until browned. Add the cumin, paprika, beef stock, and tomato paste. Cook until the liquid is reduced. Season with salt and pepper.
Remove from heat and let cool, then stir in the olives and hard-boiled eggs.

Assemble the Empanadas:

Preheat the oven to 200°C (400°F) and line baking sheets with parchment paper.
Roll out the dough and cut out round disc shapes. Place a spoonful of the filling in the center of each disc.
Fold the dough over the filling to create a half-moon shape. Use a fork to crimp the edges and seal them.

Bake the Empanadas:

Place the empanadas on the prepared baking sheets. Beat an egg with a tablespoon of water and brush the empanadas with the egg wash.
Bake for about 20-25 minutes or until golden brown.

Serve:

Allow to cool for a few minutes before serving. Empanadas can be enjoyed warm or at room temperature.