Halve and stone the apricots. Place the butter and sugar in a large non-stick frying pan and set over a low heat. Stir until the butter has melted, then mix in the halved apricots, making sure that they are well coated.
Keep stirring until the sugar has melted and the apricots are beginning to exude their juice.
Cover and cook gently, stirring occasionally, for 8 minutes or until the apricots are tender but not mushy. Then remove from the heat and add the rosewater to taste.