To make the crust, place the flour, salt, and cheese in a food processor. Add the shortening and process for 15 seconds. Sprinkle the water through the food chute, 1 tablespoon at a time, just until a dough forms. Shape into a ball and divide in half. Chill for 30 minutes. Roll and cut into 4- to 5-inch circles.
To make the filling, put the ground beef in a large skillet and saute until almost cooked. Add the onion and red and green bell peppers. Continue to cook until the meat is done and the onion is translucent. Stir in the picante sauce, potato chips, taco seasoning mix, cheese, and garlic powder. Cook until heated through. Let the mixture cool slightly before filling the pastries.
Place a little filling in the center of each pastry circle. Brush the edges of the dough with the egg-water mixture. Fold the dough over the filling, seal, and crimp with the tines of a fork. Heat ¼ inch oil in a large skillet and fry the pastries until lightly browned, about 2 minutes per side.