Preheat the oven to 200C/gas mark 6. Halve the aubergine and rub the insides with olive oil, a pinch of salt and half the garlic. Make three or four diagonal slices, about 1 to 2cm deep, across the flesh of each aubergine half. Do the same in the opposite direction. Grind a bit of pepper over the top, place on a roasting tray and pop into the oven for about 30 minutes, or until really tender right the way through. Add the whole red peppers in a tray alongside the aubergine.
Once cooked, set the peppers aside to cool, and put the aubergines in a blender and whizz to a fine puree, or finely chop them, skin and all, until you have a fairly fine paste. You can do this a day in advance if you're feeling really organised.
Add the chopped aubergine to the lamb mince along with the onion, spices, breadcrumbs, chopped olives, remaining garlic and mint. Mix thoroughly and shape into four patties.
Let the burger patties rest while you make the pistachio mayo. Blitz the pistachios in a food-processor or pound with a pestle in a mortar, with a pinch of salt, until you have a smooth, peanut butter-like paste. Add the avocado, honey and oil, and whizz until smooth and creamy. Taste and add more salt and pepper, if needed. Drizzle some olive oil over the top. Refrigerate until needed.
Prepare the red pepper by tearing it into 1cm-thick ribbons, removing skin, seeds and stem. Set aside.
Heat a frying pan over a medium-high heat. Add a splash of oil, let it warm, then carefully place the burger patties in the pan. Cook for 5 minutes, or until nicely browned on each side. If needed, press the burgers back into shape as they cook.
As soon as they're cooked, pile them into the dry burger buns to rest. The buns will act like little sponges to soak up all those lovely juices. Serve the burgers with a dab of the pistachio mayo, the roasted red pepper ribbons and a handful of leaves.