Heat the butter in a large, heavy-based frypan or saucepan over a modest flame and fry the onion until it is starting to brown.
Add the celery and carrot and cook another few minutes, stirring often, to soften.
Add the meat, perhaps a little at a time, and fry that too.
Add the thyme, bay leaf and Worcestershire and cook another minute or two.
Pour in the stock and turn right down and simmer, at least 40 minutes, preferably an hour, to soften.
Taste for salt and pepper and pour into a 2-litre casserole dish or similar.
Preheat the oven to 200°C.
To make the topping, mix the hot mashed spuds with the cheese, butter, mustard and horseradish and stir to combine.
Spread this mash all over the mince in the casserole dish and scrape the top with a fork or similar to get lots of peaks and troughs.
Bake in the centre of the oven for about 30 minutes or until the pie is browned and starting to bubble up from the edges.
