To make the filling: In a large skillet, heat the butter. Add the onions, carrots, garlic, cumin and cook for about 6 minutes over medium heat.
Add the shredded chicken and chicken broth, stir well, and cook for about 2 minutes. Add the peas, season with salt and set aside.
To make the dough: Place the flour and salt in a food processor.u2028Add the butter, and water until a dough forms.
Form a ball, cover with plastic wrap and place in the refrigerator for about 30 minutes.
On a lightly floured surface, roll out the dough into a thin rectangle. Cut out round disc shapes with a round cutter or a small plate.
Fill empanada discs with chicken mixture. Brush the edges with egg and seal in the filling by pressing the edges together to form a half moon.
Preheat oil in a deep pot to 375 degrees F. Fry the empanadas in the oil for about 3 minutes on each side. Remove from the oil and drain on paper towels.