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A few hours before you want to eat, make the dough. Mix the flour, yeast, sugar, thyme, if using, and 2 tsp salt in a bowl with your fingertips. Pour over the milk, olive oil and 100ml lukewarm water and, still using your fingers, combine to make a dough. Tip onto a work surface and knead for 8-10 mins (or blitz in a stand mixer for 5 mins). Clean, then lightly oil a bowl, put the dough in the bowl and cover with a tea towel. Leave to rise for 1 hr or until nearly doubled in size. If you want to give yourself more time, the dough will take longer to rise in the fridge (at least 2 hrs).
Divide the dough into eight equal pieces. One at a time, on a lightly floured surface, roll out to circles about 20cm wide, then brush with a little more olive oil and cook on the hot side of the barbecue for 2-3 mins on each side until puffed up and blistered. Alternatively, heat a frying pan or griddle (or two if you can) over a medium-high heat and cook, one by one in each pan, until bubbles appear on the surface after 1-2 mins. When the underside is golden, flip and cook for another 2-3 mins. Continue until all the pittas are cooked, wrapping them in foil as you go to keep warm.