Mix the Greek yoghurt and lukewarm water in a small bowl. Place the flour and yeast in the bowl of your food processor, mix, then add the yogurt-water mix and sugar, and mix again.
Add the salt and olive oil, then restart the food processor. Once a ball has formed, collect the dough and knead it with your hands until smooth and slightly sticky.
Place the ball in a large bowl and drizzle a little olive oil over it (to prevent the dough from crusting), which you spread with a pastry brush.
Place a sheet of cling film on top (no air should get through - you can use a bee-wrap if not) and leave the dough to rest for an hour in a warm place (around 85°F/30°C).
Roll out the dough on a floured work surface and cut into 4 roughly equal pieces. Use your hands to shape the dough into balls and place them back into the bowl. Tape it down again and leave to rest for another hour.
Heat your oven to 500°F/260°C on natural convection/static heat high and low. Once hot, wait a good 5 minutes, during which time remove the first dough piece and shape it into a ball with your hands. Using a lightly floured rolling pin, gently roll out the dough directly onto a sheet of parchment paper. Cover the remaining dough pieces with a clean kitchen towel to prevent them from crusting.
Place the sheet on an oven tray, right in the middle (in height and width). Wait in front of it, and the show is magical: in about 3 minutes (sometimes 3 min 30), the bread will puff up like a little balloon.
Take the first pita out of the oven, roll out another loaf and bake. It's crucial to roll out the dough pieces one at a time and bake them one at a time too. Repeat until you've used up all the ingredients.