Heat the oil in a large frying pan over a medium-high heat and brown the mince, breaking it up with a wooden spoon until there is no pink left.
Add the onion and carrot and cook for 5 minutes until the onion has softened and the mince has picked up some colour.
Sprinkle over the flour and stir for a minute, then crumble in the stock cube and add the Worcestershire sauce. Pour in 300 ml of hot water, stir, and let it bubble until the gravy thickens, about 3 minutes. Season with salt and pepper.
Turn the heat down to low and let the mince simmer gently for 15 minutes while you cook the potatoes, stirring now and then.
Meanwhile, put the potatoes in a pan of cold salted water, bring to the boil and cook for 15 to 20 minutes until a knife slides in easily. Drain well and let them steam dry in the colander for a minute.
Serve the mince and its gravy with the potatoes alongside so everyone can mash theirs into the sauce, or spoon the mince over the top if you prefer it plated properly.