Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the oil in a frying pan, add the beef a few pieces at a time until all the meat is in the pan, then fry over a high heat, stirring, until browned. Scoop the beef out of pan with a slotted spoon and transfer to the slow cooker pot.
Add the onion to the pan and fry, stirring, for 5 minutes or until softened and just beginning to turn golden. Stir in the flour, then gradually mix in the stock. Add the Worcestershire sauce, tomato purée, mustard and leaves from 2 sprigs of the rosemary. Season and bring to the boil, stirring.
Add the diced vegetables to the slow cooker pot. Pour the onions and sauce over them, then cover with the potato slices, arranging them so that they overlap and pressing them down into the stock. Sprinkle with the leaves torn from the remaining stem of rosemary and a little salt and pepper.
Cover and cook on high for 7–8 hours until the potatoes are tender. Lift the pot out of the housing using oven gloves, dot the potatoes with the butter and brown under a hot grill, if liked.