Whisk the flour and salt together in a large mixing bowl.
Add the softened butter. Use a fork to press and work the butter into the flour until it is evenly distributed and the mixture resembles coarse crumbs with no large pieces of butter remaining.
Combine the sourdough discard and warm water in a separate bowl or measuring cup. Pour the mixture into the flour. Use a Danish dough whisk or your hand to mix until all the flour is moistened and a rough, shaggy dough forms.
Turn the dough onto a lightly floured work surface. Knead by pressing the dough forward with the heel of your hand, folding it back over itself, and turning it slightly before repeating. Knead for 5–7 minutes, until the dough becomes smooth, soft, and elastic. It may feel slightly tacky at first, so continue kneading before adding more flour. If it is still sticking heavily to your hands and the counter after several minutes, dust the work surface with a small amount of flour.
Weigh the finished dough and divide it into 8 equal portions, approximately 54 grams each.
Working with one portion at a time, pull the outside edges toward the underside to begin forming a round ball. Place the dough seam-side down on an unfloured section of the counter. Loosely cup your hand around the dough and move your hand in small circles, allowing the dough to roll against the counter. The friction between the dough and the counter will tighten the surface and form a smooth, round ball. Repeat with the remaining portions.
Arrange the dough balls on the counter or a tray with enough room between them that they do not touch. Cover them with a damp kitchen towel and let them rest for 30 minutes. This rest relaxes the gluten so the tortillas can be rolled thin without shrinking back.
Preheat a dry cast-iron skillet or griddle over medium heat. Allow it to heat thoroughly before cooking the first tortilla. Do not add oil or butter to the pan.
Lightly flour the work surface and rolling pin. Place one dough ball on the counter and flatten it gently with your palm. Roll from the center outward, turning the dough frequently to encourage an even circle. Continue rolling until the tortilla is approximately 8 inches across and thin enough that you can almost see light through it. Keep the remaining dough balls covered while you work.
If the tortilla repeatedly shrinks back while you are rolling it, cover it and let it rest for another 5–10 minutes before continuing. Avoid adding more flour than necessary, as too much flour can dry out the tortillas.
Carefully lift the rolled tortilla and place it flat in the preheated skillet. Cook for 20–40 seconds, until bubbles begin forming across the surface and a few light brown spots appear underneath.
Flip the tortilla and cook the second side for another 10–15 seconds. Remove it while it is still soft and flexible. Deep browning or a long cooking time can make the tortilla dry and crisp.
Immediately place the cooked tortilla inside a clean folded kitchen towel and cover it completely. The trapped steam helps soften the tortilla and keeps it flexible.
Repeat the rolling and cooking process with the remaining dough balls, stacking each cooked tortilla inside the towel. Adjust the heat as needed. Raise it slightly if the tortilla does not begin bubbling within about 20 seconds, or lower it if dark spots develop almost immediately.
Notes
This recipe is written for a 100-percent-hydration sourdough starter made with equal weights of flour and water. Either active starter or unfed sourdough discard can be used.
Tortillas are an unleavened bread, so the sourdough is not included to make them rise. It adds subtle fermented flavor and contributes to their tender texture.
Large bubbles are normal and indicate that the tortilla was rolled thinly and the skillet was properly heated.
Storage
Allow the tortillas to cool completely. Keep them stacked, wrap the stack in a clean, dry kitchen towel, and place it inside an airtight bag or container. Store at room temperature for 2–3 days or refrigerate for up to 2 weeks.
Freeze the tortillas for up to 3 months for the best texture. Place parchment paper between them if you want to remove and thaw only one or two at a time. Thaw overnight in the refrigerator or briefly at room temperature, then warm in a dry skillet until soft and flexible.