Before You Start
If bread is fresh, leave out overnight to dry. Substitute challah bread for brioche, if desired.
In the mixing bowl of a stand mixer, add all the ingredients. Using the dough hook, knead the dough for 5 minutes. Remove the dough from the mixing bowl and place into a greased container large enough to allow the dough to double in size. Cover with plastic wrap and let the dough rise until doubled in size. Place the solid pan in the steam oven on rack position 1. Turn the steam oven on by selecting the Convection Steam Mode set to 230°C. Divide the dough into 8 equal pieces and gently flatten each piece into a thick disc. Cover with plastic wrap or a dishcloth. Using a rolling pin, roll one piece of dough into a 20 cm circle. Dust the dough and countertop with flour to ensure that the pita bread does not stick.
After the oven is preheated, slide the rolled-out pita bread onto a floured pizza peel. Open the steam oven door and slide the pita dough off the pizza peel onto the solid steam oven pan. Work quickly and shut the door. Set a timer for 3 minutes. While the first pita bread is baking, roll out the next pita. The pita bread should inflate into almost a ball. After 3 minutes, remove the baked pita from the oven and place in a large bowl. Cover the bowl with foil to allow the pita bread to soften. Repeat with the remaining pita dough, each time adding the baked pita bread to the bowl and covering again. Deflate the pita bread if necessary.