Pour the flour into a food processor. Cut the butter into 12 to 16 even-sized pieces and add them to the flour. Pulse the food processor until the butter is about the size of peas. In a separate, small bowl, mix the water and the egg until it is homogenous and add the mixture to the flour and butter. Pulse until the mixture just begins to hold together when you squeeze it in your hand. Add slightly more water, if needed, but do not over mix. Remove the dough, flatten, and wrap it in plastic wrap. Let chill for 1 hour or overnight.
Roll the dough out on a floured board to slightly less than ⅛ inch. Cut the dough into rounds using a cutter, bowl, or a plate. (I prefer the empanadas large so cut the dough out about 3½ inches across.) Top each dough round with some of the chilled empanada filling. (When first preparing the recipe, it may be easier to seal the empanadas to avoid over filling them, but as you gain experience you can add slightly more filling.) Moisten the edges of the dough round with a beaten egg to help them stick. First, fold over the dough to create a turnover and then using a fork you can seal the edges further with a decorative marking. This is perhaps the simplest way to seal the pastry. Brush the pastry with egg wash (1 beaten egg mixed with 1 tablespoon of water) and transfer the pastry to a greased baking sheet while you complete filling the empanadas.
Preheat the oven to 400ºF.
Place the finished empanadas in the oven to bake for about 20 minutes, or until the pastry is golden. Let cool slightly before serving.