Tip the mince, diced lamb, the spices, garlic, 1 tsp freshly ground black pepper and 1 tsp salt into a large food processor. Blitz to a paste – the mixture should resemble pâté. Lightly oil a sheet of foil and lay it on a chopping board. Tip the meat mix onto the foil, and tightly roll up into a large, roughly 10cm-wide sausage. Twist the ends shut so they’re sealed well, then chill for a few hours, or until firm. Can be prepared up to a day ahead.
Heat the oven to 160C/140C fan/gas 3. Put the foil-wrapped kebab in a roasting tin, then pour 100ml water around it. Bake for 1 hr 10 mins, turning occasionally, or until a meat thermometer inserted in the middle reads at least 65C. Remove from the tin and leave to cool, then transfer to the fridge and chill overnight.
Light a barbecue or heat a gas barbecue to medium (see tip, below). When the flames have died down and the coals are ashen, unwrap the kebab and push two large skewers through the middle. Sit the kebab directly on the grill, and close the lid, if the barbecue has one. Cook until heated through and well browned, turning occasionally – this will take about 30 mins.
Using a sharp knife, finely carve slices from the sides of the kebab. If you like, you can then return the rest of the kebab to the barbecue to brown further, or carve it all at once. Serve the meat on the flatbreads with the chillies, lettuce, tomatoes and onions in separate bowls for everyone to build their own wrap, plus the chips on the side.