To prepare your sourdough starter for making homemade sourdough tortillas, add one tablespoon of starter from your most recent batch of active starter or discard to a 1-pint jar or similar container. Then add water and fresh white flour (all-purpose or bread flour can both be used to feed a starter). Mix well, and leave at room temperature. Let the starter sit at room temperature for 6 to 12 hours until it is doubled in volume, full of large bubbles, and smells fragrant like ripe fruit.
Boil about 2 cups of water. Add about 1 1/2 cups of the hot water to a heat safe measuring carafe. Put a thermometer in the water to measure the temperature. Add cooler water to the carafe until the temperature range is 110 to 120 degrees F.
Place a mixing bowl on the kitchen scale and tare the weight. Add the very warm water, bread flour, salt, and active starter.
Mix with a spoon or with a dough hook attachment if using a stand mixer.
Knead this dough by hand or with a dough hook in a stand mixer on medium-low speed for 6 to 10 minutes. The dough should pull away from the bowl or work surface, it should look smooth, bounce back when poked with a finger, and when you bend the dough it shouldn't break apart easily, it should be elastic.
Once your dough has reached this stage, it is time to knead in the softened unsalted butter or lard until the fat is completely incorporated. This final stage of kneading will take 4 to 10 minutes depending on whether you are doing it by hand or with a machine. It should have the same characteristics as I mentioned above (not sticky, smooth, bounces back, elastic) when it is done being kneaded and ready to rest.
For this resting or bulk fermentation stage, doubling in volume isn't important. But you do want to cover the dough with plastic wrap or put in an airtight container for at least 2 hours up to 6 hours.
Place the dough on an unfloured surface.
You can divide the dough by weight or visually by rolling the dough into a log shape then using a bench knife or sharp end of a dough scraper to divide the dough into fourths. Then divide each fourth of dough into fourths again to create 16 equal pieces of dough.
Take each piece of dough and preshape by pulling the ends of the dough out and then under itself repeatedly to create a smooth round top. Pinch the ends to the bottom of the developing ball of dough to help create the tight shape and tension. Once it's completely smooth and tight, place on the top of the unfloured work surface or on a baking sheet to rest.
Continue with the rest of your pieces of dough until they are all lined up in neat rows. Cover the balls of dough with plastic wrap to seal out all air exposure and lay a kitchen towel on top of the plastic wrap to make sure the plastic is weighed down. Let the dough balls rest for a recommended 2 to 4 hours.
Heat up a large cast iron pan over medium to medium-high heat (natural gases run hotter, so start with medium) for about 10 to 20 minutes to make sure it is thoroughly heated. Place a large plate near your cooking area for the cooked tortillas.
Do not uncover all the balls of dough because they will dry out easily. While they are still covered, take off the towel temporarily and firmly hit each row of dough balls with the rolling pin 1 to 2 times. Adjust the plastic wrap if needed and put the towel back on top.
Take out one piece of dough and recover the rest with the plastic wrap and the towel. Place it on your work surface next to where your hot pan is waiting. ]
Use your rolling pin to roll out the dough from the center to the outside edges with firm pressure. Pick up the dough and rotate to roll out the other direction. Continue rolling from the center to stretch the dough into a circle. Once your dough is about 4 to 5 inches wide, begin to focus on rolling the edges thin by applying firm pressure at an angle. This is much easier with a tapered French-design rolling pin. Roll the dough until it is the same thickness across, is almost see-through (if your work surface is granite or has a pattern, you should begin to see it), and is 5 to 6 inches wide.
Add the thin, shaped tortilla to the hot pan. Let it cook for 5 to 10 seconds on the first side. The edges should be set and not give when using the spatula or flipper. Flip the tortilla over to cook on the second side for 10 to 15 seconds. Give gentle pressure around the edges of the tortilla to ensure even cooking (the pressure shouldn't leave an indentation). Then, flip the tortilla again to finish cooking the first side and to try to get the center to fill with steamy air. Gently press on the edges of the dough to try to create an air pocket. Once you see an air pocket forming, gently apply pressure to encourage the steamy air to open up more of the tortilla center. This should happen almost immediately after flipping and applying pressure so if you don't see it puffing up quickly, within 5 seconds or so, place on the waiting plate for finished tortillas.
Stack the cooked tortillas on top of each other. The hot steam will keep them soft and pliable as the others cook.
Once all the tortillas are cooked, wrap them in a tea towel or kitchen towel to keep them soft for serving. A tortilla warmer and keeper can be used to store the cooked tortillas as well. Either method (the tortilla warmer or a towel) will keep the tortillas from drying out while allowing enough steam to escape so the tortillas don't become sticky.