Using a vegetable peeler, remove the skin from the aubergines and slice them in half, top to bottom. Cut each half into 3 thick wedges.
Melt the butter with the olive oil in a wide, shallow pan over moderate heat. Place the aubergine pieces in the hot butter and oil, cover with a lid and let them cook for 7-10 minutes until pale gold on the underside. Turn each piece and cook the other side.
Peel and grate the ginger to a purée (about 1 heaped tbsp). Peel and thinly slice the garlic. Add the ginger and garlic to the pan with salt, black pepper, turmeric, and cinnamon. Let the spices sizzle briefly, then pour in the water and bring to the boil. Let it bubble uncovered for 5 minutes.
Lower the heat so the liquid bubbles gently, cover with a lid, then leave to simmer uncovered for at least 25 minutes, or until the aubergines are truly tender and silky. Trickle in the honey.
To make the yoghurt sauce, put the yoghurt into a bowl, and cut the cucumber in half lengthways. Scrape out the seeds and discard them, then coarsely grate the flesh. Squeeze the flesh to remove excess juice. Stir the grated cucumber into the yoghurt. Shred the mint leaves and stir them in. Roughly chop the pistachios and fold them into the yoghurt sauce.
Serve the aubergines warm, with the yoghurt sauce.
