Heat a frying pan large enough to hold the lamb chops with 1 tablespoon vegetable oil. Season the lamb cutlets and fry them for 3-4 minutes each side until golden brown.
In a separate pan, heat the second tablespoon of oil and fry the artichoke halves, cut side down, for a minute. Add the vinegar and cook until evaporated.
Add the butter beans, tomatoes and garlic and sauté for 2-3 minutes until both are hot and the tomatoes start to bleed. Add the olive oil and basil and season well with salt and cayenne pepper. Once the lamb is cooked place 3 chops on each of two plates, and serve the butterbean mixture alongside.