Preheat the oven to 190°C.
Prick potatoes with a fork, rub with oil, and bake for 60 to 90 minutes until tender.
Heat a pan with oil and brown the beef mince in batches.
Add onions, garlic, thyme, and celery to the pan and fry until softened.
Stir in tomato purée for 2 minutes, then add Worcestershire sauce and finely chopped carrot.
Pour in red wine and reduce by a third before adding beef stock.
Simmer the mixture for 30 minutes until the sauce thickens and the beef is tender.
Boil whole carrots in water with salt, sugar, and a knob of butter for 40 minutes.
Cool the mince mixture slightly and season with salt, pepper, and Worcestershire sauce.
Increase oven temperature to 220°C.
Extract potato flesh and pass through a ricer or mash with a fork.
Beat warm milk and half the remaining butter into the potatoes until smooth.
Transfer mince to a dish, top with mash, dot with butter, and bake for 15 minutes.
Serve the pie hot with the glazed carrots.