In the mixing bowl of a stand mixer, place the water, honey, and yeast. Allow the yeast to proof for five minutes. Add the flours and salt. Mix with the dough hook until a smooth dough ball forms. Transfer the dough to a greased bowl and cover with a tea towel. Let rise until doubled in bulk.
To make the dough in a bread machine:
Alternatively, you can use a bread machine. In the bread machine pan, place ingredients in the order recommended by the manufacturer. In my case, that means liquids first, then dry ingredients with yeast last. Set on dough cycle.
When the dough is ready, remove dough to lightly floured surface. Preheat the oven to 450 °.
Divide the dough into 12 equal-sized pieces. Roll into balls. Roll each ball into a 5-inch circle and rest on floured kitchen towel. Continue process. until all 12 pieces are rolled.
Place two rounds on a baking sheet and bake for 2 minutes. Flip and bake another 1 ½ to 2 minutes. Do not brown. Dough will puff during baking. Cool on a rack.
Continue the process, allowing oven to reheat for another couple minutes in between batches. Serve immediately. These taste best the day they are made.
Notes
Nutritional values are approximate and based on 1 pita bread.