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In a medium bowl, whisk together the flour, baking powder, and salt.
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Using your fingers or a pastry blender, work the lard or butter into the flour mixture until no visible pieces of fat remain. (If you’re using vegetable oil, add it in step 3.)
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Add the starter and 4 tablespoons (57g) hot water (plus the oil, if you’re using it) and stir briskly with a fork or dough whisk until a shaggy dough comes together. Gradually stir in up to 2 tablespoons of additional water if needed to bring the dough together.
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Transfer the dough to a lightly floured work surface and knead briefly, just until the dough becomes cohesive. If the dough is very sticky, gradually work in a bit more flour, a dusting at a time.
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Divide the dough into 8 pieces (about 75g each). Round the pieces into balls and flatten slightly; coat with nonstick spray to prevent drying out. Cover and let rest for 20 to 30 minutes (see “tips,” below).
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While the dough is resting, preheat a dry large cast iron griddle or skillet or an electric griddle over medium-high heat, about 400°F.
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Working with one piece of dough at a time, roll the dough out to a 7" to 8" round on a lightly floured work surface, dusting with more flour as needed to prevent sticking. (Keep the remaining pieces of dough covered while you work.) Cook the tortilla in the preheated pan for 60 to 80 seconds on each side, until opaque, with some charring and bubbling.
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Wrap the tortilla in a kitchen towel as it comes off the griddle to keep it warm and pliable. While one tortilla is cooking, roll out the next, repeating until all the tortillas have been cooked.
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Serve the sourdough tortillas warm or at room temperature. If there are any leftovers, allow the tortillas to cool completely, then wrap them tightly in plastic and store in the refrigerator for up to 4 days. Reheat in a dry skillet until warmed through, or wrap in a kitchen towel and heat in the microwave in 5-second increments.