For the mash, heat the butter and two tablespoons of the olive oil in a large frying pan over a very low heat. Add the onion and cook for about 15 minutes until very soft and golden.
Stir in the garlic, half the thyme and the paprika and cook for a further five minutes.
Bring a pan of water to the boil, then add the chickpeas and heat through for 2-3 minutes. Drain well.
In a food processor, blend together the chickpeas, three-quarters of the caramelised onions, the lemon juice and the remaining olive oil to form a smooth purée.
Season well with salt and freshly ground black pepper, then return to the saucepan and keep warm. (Alternatively, you can blend all the ingredients in the pan using a hand-held blender.)
Meanwhile, for the lamb cutlets, heat another large frying pan over a high heat. Season the lamb cutlets with salt and freshly ground black pepper and drizzle over the olive oil.
Cook the cutlets in batches, adding them to the hot pan to quickly sear on both sides, then reduce the heat to medium and fry for a further two minutes on both sides (for rare), 2-3 minutes on both sides (for medium) or 4-5 minutes on both sides (for well done).
Remove the cutlets from the pan and leave to rest, covered in foil to keep warm. Drain the fat from the pan and then stir in the wine, scraping up any browned bits from the bottom to deglaze.
Allow the liquid to bubble and reduce for a few minutes, then add the stock, vinegar and remaining thyme. Simmer for 3-4 minutes until reduced and slightly thickened.
To serve, spoon some of the chickpea mash onto each plate, arrange the lamb cutlets on top, drizzle over the sauce and scatter with the remaining caramelised onions.