Preheat the oven to 200C/400F/Gas 6.
Boil the artichokes in salted water for 6-8 minutes, then drain.
For the rosemary and lemon artichokes, heat the oil and butter in an ovenproof frying pan and fry half the artichokes for 1-2 minutes. Squeeze over the lemon juice and add the lemon halves to the frying pan. Add the olives and rosemary and transfer to the oven to roast for 6-8 minutes.
Meanwhile, for the chilli-olive artichokes, heat the butter and chilli flakes in an ovenproof frying pan and fry the remaining artichokes for 1-2 minutes. Squeeze over the lemon juice and add the olives to the pan. Transfer to the oven to roast for 6-8 minutes.
Serve the artichokes on separate plates with the pan juices drizzled on top.