Combine the lukewarm milk and water with the sugar, yeast, and oil in a bowl and cover with plastic wrap. Set the bowl aside for 15 minutes for the yeast to get active.
You can use a stand mixer or make the dough by hand, according to that, use a stand mixer bowl or a large mixing bowl. Place the flour and the salt in that bowl and whisk to combine them.
Gradually add small quantities of the active yeast mixture to the flour and stir continuously with a bread whisk until you have used all the yeast mixture and have a soft dough formed.
Transfer the dough on your working surface and knead for 4-5 minutes until the dough becomes smooth.
Brush a large bowl inside with oil and place the dough inside. Cover with plastic wrap or a tea towel and let the dough rest for 40 minutes until it rises and doubles in size.
Press on the dough to remove air and cut it into 8 even pieces. Roll each piece of dough into a ball.
Place one ball of dough on a lightly oiled working surface and use a rolling pin to roll it to a round dough piece, roughly about 20 cm in diameter in size.
You can cook the Greek pitas on the hob or on a live fire. Heat a cast-iron plate or a large heavy-based pan on moderate heat. If using a cast iron plate, brush it with oil, or pour one tablespoon of oil into the pan, and cook the pitas on each side for 1-2 minutes until the pitas puff up slightly.
Cut the Greek pitas into small pieces and serve with a dip as a snack, or make wraps with the pita bread stuffed with grilled meat or falafels, garnished with salads and sauces..