For the mince, heat the oil in a large casserole dish over a high heat. Add the onions and fry for 3-4 minutes, or until softened.
Add the stock cubes and stir well to dissolve them in the oil. Fry for a further minute.
Add the mince, in batches, and fry for 6-8 minutes, stirring, or until browned all over. Remove the cooked mince and set aside on a plate. Repeat the process with the remaining mince.
Return the cooked mince to the casserole, then add the Worcestershire sauce and water and bring the mixture to a simmer.
Add the gravy browning powder and season, to taste, with salt and freshly ground black pepper. Cover the casserole with a lid and simmer for three hours, stirring occasionally, or until the cooking liquid has thickened and the meat is tender.
Meanwhile, for the dumplings, in a large mixing bowl, mix together the flour and chopped parsley. Season, to taste, with salt and freshly ground black pepper.
Gradually add the water in a thin stream, stirring well, until the mixture comes together as a firm dough. (NB: You may not need to use all of the water.)
Turn the dough out onto a lightly floured work surface and knead lightly until smooth. Pinch off golf ball-sized pieces of the dough and roll into balls.
Boil the potatoes in a pan of salted water for 10-15 minutes, or until tender.
As the potatoes are cooking, carefully lower the dumplings into the boiling water. When all the dumplings have been added to the pan, reduce the heat until the mixture is simmering, then cover the pan with a lid and simmer for 12-15 minutes, or until the dumplings have risen and the potatoes are just tender.
Remove the dumplings from the pan using a slotted spoon and set aside to drain on kitchen paper, then drain the potatoes and return them to the pan. Add half of the butter and stir until the butter melts and coats the potatoes.
Meanwhile, bring a pan of salted water to the boil, add the carrots and cook for 4-5 minutes, or until tender. Drain well, then return the carrots to the pan and stir in the remaining butter. Season, to taste, with salt and freshly ground black pepper.
To serve, spoon the dumplings into the centre of each of 12 serving plates. Spoon over the mince. Serve the buttered potatoes and carrots alongside.