Oven-Puffed Whole Wheat Feta Parmesan Pitas

Steps

1. Set aside about 20 g of the bread flour for dusting. In a large bowl, stir the lukewarm water, honey and instant yeast together.
2. Add the whole wheat flour, the remaining bread flour and the salt, and mix into a shaggy dough. Rest 15 minutes so the bran softens.
3. Add 20 g of the olive oil (most of it, keeping the last 5 g for the bowl) and knead 8 to 10 minutes until smooth and slightly tacky. This is about 69% hydration and 1.1% salt; the feta adds more salt.
4. Flatten the dough, scatter the crumbled feta over it, fold it up and knead 1 to 2 minutes until the feta is evenly spread through.
5. Rub the bowl with the remaining 5 g of olive oil, turn the dough in it, cover, and let rise at about 75°F (24°C) for 60 to 75 minutes, until doubled in size and it springs back slowly when poked.
6. While the dough rises, put a baking sheet or baking stone on the lowest oven rack and preheat to 475°F (245°C) for at least 45 minutes.
7. Divide the dough into 12 equal pieces (about 92 g each), shape into balls, cover and rest 10 minutes.
8. Using the reserved bread flour for dusting, roll each ball into a round about 6 inches across and 1/4 inch thick, keeping the thickness even so it puffs. Lay them on a floured towel, cover and rest 15 minutes.
9. Sprinkle a pinch of the Parmesan over the top of each round and press it in lightly, using all of the Parmesan across the 12 rounds.
10. Working in batches, lay 3 or 4 rounds directly on the hot sheet or stone and bake 3 to 5 minutes, until they balloon and the cheese is golden in spots; the center should reach about 200°F (93°C).
11. Move baked pitas to a rack, cover loosely with a clean towel to keep them soft, and let cool about 10 minutes before cutting open.