To make the dough, tip the flour into a bowl, stir in the sugar and 1 tsp salt. Add the yeast, then make a well in the centre and add the oil. Gradually pour in 350-360ml lukewarm water, then combine the ingredients to form a dough. Knead for 5 mins until smooth. Transfer to a clean bowl, cover with a damp cloth and leave in the fridge overnight.
The next day, heat oven to 240C/220C fan/gas 9. Cut the green ends off the leeks – leave the white ends so they stay together when cooking. Rinse in cold water, then dry and place on a baking tray. Roast for 25 mins, turning halfway through, until the outside is fully charred. Discard the outer layer, but leave a little char for added flavour. Trim the ends, then slice into 2cm rounds. Can be made a day ahead and chilled. Leave your oven on and put in two flat baking sheets (or a pizza stone, if you have one).
To make the cheese sauce, melt the butter in a saucepan over a medium heat, then whisk in the flour. Pour in a third of the milk and whisk until smooth. Repeat twice with the remaining two-thirds. Turn the heat right down and cook for 15 mins, whisking occasionally, until it has the same consistency as double cream. Whisk in both cheeses – the halloumi won’t melt – and add sea salt to taste. Pour the sauce into a baking tray and allow to cool completely. Can be made a day ahead and chilled.
Heat the oil in a deep-fat fryer or heavy-bottomed pan to 160C. Slice the potatoes into approx 1mm slices on a mandolin. Rinse in warm water to remove excess starch, then dry with a cloth. Fry in small batches for 3-4 mins until golden (add the slices one at a time so that they don’t stick together). Transfer with a slotted spoon to a baking tray lined with kitchen paper. Season with fine salt.
To make the pides, knock back the dough on a floured surface, roll into a long sausage shape and cut into six equal pieces. Roll each piece into a ball and cover with a damp tea towel.
Roll out a ball of dough on the floured surface into a large oval (approx 40 x 15cm) as thick as a 50p piece – it will be very elastic but will roll out eventually. Transfer to a floured baking sheet to assemble the pide.
Leaving a 3cm border, spread a sixth of the sauce down the centre of the pide. Sprinkle over the sesame seeds and oregano, and top with leeks. Fold into a canoe shape, leaving the centre of the filling exposed. Pinch the ends to avoid unravelling when baking, and push down on the dough to ensure that it keeps its shape.
Slide the pide onto one of the hot baking sheets. Bake for 12 mins until it has a golden, crisp exterior. Meanwhile, assemble the next one and bake on the other hot tray. Continue until all the dough is used up, setting the pides aside when they’re done.
Once they’re all baked, reheat them for 2-3 mins, brush the outside with melted butter, arrange a line of potatoes down the middle and sprinkle over the crumbled cheese.