In a large bowl or the bowl of your stand mixer, stir together the bread flour, whole wheat flour, sugar, instant yeast, and kosher salt. Make a well in the centre and add in the sourdough starter discard, water, and olive oil and mix into a shaggy dough. Knead the dough until smooth and springy, about three to four minutes, adding more flour if needed, then transfer to a lightly greased bowl, cover with a dinner plate, and set in a warm place to rise for one to two hours or until doubled in size.
When the dough has risen, punch it down, turn it out onto a lightly floured work surface, and divide it into six equal pieces. Roll each piece into a six millimeter to one centimeter thick oval or round then place on a large baking sheet lined with parchment paper. Cover with a clean kitchen towel and set back in the warm place for 30 minutes to rise.
Meanwhile, preheat your oven to 500ºF. When the pitas have risen and are a little puffy, bake them in the preheated oven for five to six minutes or just until very puffy but not yet golden.
Remove the pita to a wire rack to cool slightly or completely before digging in.
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