Mix the garlic, lemon, chilli and olive oil together, put the lamb cutlets in a dish and pour over the marinade. Cover and leave to marinate for 1 hr in the fridge, if you have time. Tip the broad beans into a food processor with half the olive oil, plenty of salt and pepper, and the lemon juice. Blitz to a chunky purée, then tip into a saucepan but leave off the heat.
Heat a griddle pan and cook the lamb for 2-3 mins on each side for thinner chops, 3-4 mins on each side for thicker chops. While the chops cook, gently heat the purée. Then stir through the mint and the rest of the olive oil. Check for seasoning. Serve the lamb in a pile with a bowl of the smashed broad beans and plenty of bread to mop up the juices.