Combine the sugar, yeast, water and milk in a bowl. Set the bowl aside for 5-10 minutes, until the mixture starts to froth.
In another bowl, combine the flour, the salt and the chopped fresh thyme leaves and give it a mix to combine.
Add the oil to the yeast mixture and stir to combine.
Add the yeast mixture to the flour mixture in batches. Make sure each batch is incorporated before adding the next.
Transfer the mixture to a lightly floured working surface. Knead for 4-5 minutes until the dough becomes smooth.
Brush a bowl with some oil and add the dough.
Cover with a towel and let it rest on the oven for about 40-60 minutes until it rises and doubles in size.
Press on the dough to remove the air and cut it into 6 equal-sized pieces.
Place pieces of dough on a lightly oiled working surface. Use a rolling pin to roll out each piece of dough to a circle 8 inches in diameter.
Cook the pita bread over medium heat for 1-2 minutes on each side in the pan, until they puff up slightly.
Cut each pita into 4 - 6 pieces.
Transfer to a plate and serve with chicken or pork gyro, sausages or vegetables. Sprinkle with chopped thyme.
