Trim any woody bases from the sprouts then shred finely. You can do this by hand, using a handheld mandolin or use the shredding attachment on a food processor.
Take a large frying pan or saucepan and place over a medium-high heat. Add the lardons into the pan while it's still cold, then let these render and fry for 7 mins until crisp. Reduce the temperature a little, add the shallot and soften for 5 mins without colouring, stirring occasionally.
Add the garlic, the chopped anchovy fillets and cook for 2 minutes until the anchovies start to 'melt'. Add the sprouts and cook for 2-3 mins, stirring occasionally, just until the sprouts change to a vivid and glossy green.
Add the cream, 100ml water, the cheese plus the thyme, black pepper and nutmeg. Allow the liquid to bubble up and warm through for 1-2 mins maximum (you don't want to overcook the sprouts). Remove from the heat and decant into a gratin dish or low-sided casserole (around 2 litres).
Make the crumb by melting the butter in a frying pan, add the breadcrumbs and coat. Fry gently until just starting to turn golden. Remove from the heat and add the parsley, walnut pieces, lemon zest and seasoning. Spread evenly over the sprout mixture.
Heat the oven to 200°C/180°C fan/gas mark 6 then bake for 20-25 mins or so, until the crumble layer is browning and the cream is bubbling through. Take out of the oven, allow to rest for five minutes and serve.