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In the bowl of a stand mixer, add the flour and salt. Give it a quick stir with the dough hook to distribute evenly.
Pour in the sourdough discard, olive oil or tallow, and warm water. Mix on low until the dough begins to come together. If the dough feels too sticky, add a tablespoon of flour at a time. If it’s dry and crumbly, drizzle in a little more water.
Let the mixer knead the dough for 2–3 minutes until smooth and elastic.
Cover and let the dough rest for 10 minutes.
Transfer the dough to a floured surface. Divide into 16 equal pieces, then roll each into a smooth ball.
Use a rolling pin to flatten each dough ball into a very thin round—aim for about 6–7 inches wide.
Preheat a dry cast iron skillet or griddle over medium-high heat. Cook each tortilla for 30–45 seconds per side, until you see bubbles and light golden spots.
Place finished tortillas in a clean tea towel and cover to trap steam.