Heat 1 tbsp oil in a large saucepan or Dutch oven over medium-high heat, and cook the beef until browned. Once browned (it doesn't have to be fully cooked through), scoop up the beef with a slotted spoon and set aside.

Add a little more oil into the pan if it's looking dry, and add the onion, carrots, and celery. Cook over medium-low heat until soft, about 15-20 mins. Add the garlic, flour and tomato paste, increase the heat to medium and cook for 2-3 minutes more, then return the beef to the pan. Pour in the wine, if using, and boil for 2-3 minutes to reduce it slightly. Add the stock, Worcestershire sauce, thyme, and bay leaves. Bring to a simmer and cook, uncovered, for about 45 mins. The beef mixture is done when most of the liquid has evaporated and the sauce becomes thick, like the consistency of gravy, and coats the meat. Check after about 30 mins: if a lot of liquid remains, increase the heat slightly to help reduce the gravy. Taste and season with salt and pepper, if desired, then discard the bay leaves and thyme stalks.

As the beef mixture simmers, make the potato mash. Place potatoes in a large pot and cover with cold salted water by 1 inch. Bring to a boil, then reduce heat and simmer until tender, about 10-15 minutes. Drain well, then allow the potatoes to steam-dry for a few minutes. While you're waiting, preheat the oven to 400°F. Mash the potatoes with the milk, butter, about 3/4 of the cheese, and the nutmeg. Taste, and season with salt and pepper if desired.

Spoon beef mixture into a 12"x8.5" baking dish. Spoon the potato mash on top of the beef to cover. Sprinkle the remaining cheese on top (add more cheese, if desired). Bake in the oven at 400°F for 25-30 mins, or until the topping is golden brown and the gravy is bubbling at the sides.