Place the flours, salt, and baking powder into a food processor and pulse to combine.
Add the butter (or ghee) and pulse until coarse crumbs form.
Add the sourdough starter and pulse until combined.
Turn on the food processor and slowly drizzle in the warm water just until a dough ball forms. You may not need to use the entire half cup of water.
Turn the dough out onto a floured board and knead a few times until it's soft.
Wrap the dough in plastic wrap (or beeswax wrap) and set aside to rest at room temperature for at least 4 hours and up to 24 hours.
When you're ready to make the flatbread, remove the dough from the plastic wrap and divide it into 6-8 roughly equal-sized pieces.
Flatten each dough piece into a disc, then roll the disc about ¼” thick, using a sprinkle of flour to prevent sticking if necessary.
Heat a cast iron skillet over medium-high heat. Allow it to get very hot. Then, place one flatbread dough into the dry skillet and cook for 1-2 minutes until bubbles start to form. Flip and cook on the other side for an additional minute. Remove the flatbread from the skillet and repeat the rolling and cooking with the remaining discs.
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Notes
You’ll want to start this recipe at least 4 hours ahead of time and up to a full day ahead of time.
A higher ratio of whole wheat flour can be used if desired. Even 100% whole wheat flour is ok.