Put the flour, shortening, baking powder, and salt in food processor. With the machine running, add the water through the feed tube; process just until a soft dough forms. Divide the dough into 6 pieces and shape each into a ball. Roll each ball out between sheets of plastic wrap into a 6-inch round.
Set a medium nonstick skillet over medium heat and heat until a drop of water sizzles in it. Reduce the heat to medium-low. Add a dough round and cook until speckled and slightly puffed, about 1 1/2 minute on each side. Transfer the tortilla to a plate lined with a clean kitchen towel; fold the towel over to keep the tortilla warm. Cook the remaining dough rounds to make a total of 6 tortillas, stacking them in the towel as they are cooked.
To reheat the tortillas, wrap each one in a separate paper towel or napkin and microwave on High until heated, about 5 seconds for each tortilla.
