Sieve the whole wheat flour through a fine mesh sieve into a medium bowl; discard any remaining bran (any dark, reddish-coloured flakes or pieces), or feel free to save it for other recipes. Add the bread flour to the bowl. Add the yeast and salt and whisk to combine. 

Tip: If using fresh yeast, dissolve it in the water first and then follow the instructions in the next step.

Place the water, olive oil and honey into a second medium bowl. Whisk until the honey dissolves. Add half of the flour to the water mixture and stir with a whisk until a smooth batter forms. Add the remaining flour and whisk or knead by hand until the dough is uniform and no dry flour remains. Cover with a damp towel or cling film and let sit for 30 minutes.

Using lightly moistened hands, gently knead the dough in the bowl until it tightens, about 10 to 20 seconds. Gather the dough into a smooth ball. Cover the dough with a damp towel or cling film and let it sit at about 24 °C (75 °F) for 60 to 120 minutes. 

Tip: The dough should become puffy and expand to 1 ½ times in volume.

Transfer the dough to a lightly floured surface. Using a dough scraper and digital scale for accuracy, divide it into roughly four 200-gram pieces (for thicker pitas) or eight 100-gram pieces (for thinner pitas). Shape each piece into a tight, smooth ball. Pay special attention to sealing up the seams on the underside as tightly as possible.

Drizzle the now-empty dough bowl with olive oil. Dip each dough ball into the bowl and use your hands to evenly coat the ball's exterior in oil. Transfer the dough balls to a lightly oiled dough box, tray or individual containers, seam side down. Cover tightly and refrigerate for 8 to 24 hours.

The next day, fire up your oven, aiming for 315 to 370 °C (600 to 700 °F) on the pizza stone inside. Use an infrared thermometer to quickly and accurately check the temperature. Set a cooling rack into or over a rimmed baking sheet and drape a clean kitchen towel over it.

Place 120 grams of flour into a shallow, wide bowl. Gently transfer one dough ball to the flour and coat both sides in flour. Transfer the pita to a well-floured surface, seam side down. Pat the dough into a 4-inch (10-centimetre) round of even thickness using your palm and fingertips. Using a rolling pin, roll the dough into an 8-inch (20-centimetre) round, adding flour to both sides of the dough to prevent sticking. Remove any excess flour from the disk and transfer it to an unfloured pizza peel, seam side down. 

Launch the pita into the oven, setting it as far from the flame as possible, and close the oven door (if it has one). Cook until the pita puffs completely, about 30 seconds to 2 minutes (the thick pitas will take longer to puff up than the thinner ones). Using a turning peel, rotate the pita to promote even browning on the upper surface. Remove from the oven. 

Tip: If the underside of the pita is completely pale, return it to the oven and continue cooking until it’s lightly browned, up to 30 seconds.

Transfer the pita to the cooling rack and cover it with the towel. This will help prevent it from drying out or getting soggy. 

Serve immediately or cool to room temperature. You can also transfer the pita to an airtight container and save it for up to 2 days. Repeat with the remaining dough balls.