Preheat the grill to its highest setting. Slice the ciabatta in half lengthways and place, cut-side down, on a baking sheet. Grill for 1-2 minutes each side, then remove from the heat. Meanwhile, slice the mozzarella and chop the rosemary.
Arrange the artichokes and mozzarella on the ciabatta and dot on the ricotta. Drizzle with a little of the artichoke oil, then scatter over the rosemary and season well. Grill for a further 2-3 minutes until bubbling and golden. Cut each piece in half to serve.