Make the empanada dough. Add the flour and salt to a food processor and pulse until combined, about 5 pulses. Add the butter, 1 egg and the ice water. Pulse until the mixture resembles coarse crumbs, about 20 pulses. If the dough won’t come together add more ice water 1 tablespoon at a time and pulse until incorporated. Shape the dough into a ball. Tightly cover the dough in plastic wrap and place in the refrigerator for at least 30 minutes, up to 2 hours.
Meanwhile, make the filling. Fill a medium size saucepan with water and bring to a boil over high heat. Add the potato and boil until tender, about 3-4 minutes. Drain.
To a large skillet set over medium-high heat, combine the beef, onions, carrots and celery and cook, breaking the meat up with a wooden spoon, until the beef is browned and the vegetables are softened, 8-10 minutes.
Stir in the potatoes, garlic, chili powder, cumin, cinnamon, salt, pepper, peas and beef stock. Cook, stirring, until most of the liquid has been absorbed, about 5 minutes.
Prepare the dough. Remove the dough from the refrigerator and divide it into 10 equal pieces—roughly 2.2-ounces each. On a lightly floured surface, roll each piece of dough very thin into a circle roughly 7-inches wide. Add a heaping ⅓ cup of the beef mixture onto one side of each of the dough rounds.
Preheat the oven to 375°F with a rack in the center position.
In a small bowl, whisk the remaining egg. Using a pastry brush, brush the egg on the exposed edge of the dough. Fold the dough in half over the filling. Using a fork, firmly press and seal the edges together. Alternatively you can make empanada pleats. Repeat this process with remaining dough and filling, arrange on a parchment lined baking sheet.
Stir 1 tablespoon of water into the bowl with the remaining egg. Lightly brush each empanada with egg wash. Bake until golden brown, about 35 minutes. Serve warm.
Leftover empanadas will keep in an airtight container, refrigerated for up to 3 days. To freeze, cool the empanadas to room temperature, wrap tightly in plastic wrap, then store in an airtight container for up to 3 months. To reheat, place in a 300°F oven or toaster oven for about 10 minutes, or until warmed through.