Heat the oven to 190C (170C fan)/375F/gas 5. Meanwhile, whisk the eggs with half the milk and the miso paste, then set aside.
Arrange the sourdough slices in a single layer in a roasting tray and pour the egg mixture on top. Leave to soak for 10 minutes, then turn over the slices and leave to soak for 10 minutes more.
While the bread is soaking, melt the butter in a large saucepan on a medium heat. Once hot, add the celeriac, season generously, then cook, stirring regularly, until deep golden brown all over and cooked through.
Add the remaining 300ml milk to the pan, leave to simmer for five more minutes, then blend smooth.
Put half the soaked bread in the base of a deep casserole dish. Top with half the cavolo nero, followed by half the celeriac puree. Top with the remaining bread, pour any excess egg mixture on top of the bread, then top again with the remaining cavolo nero and celeriac puree.
Grate the chestnuts all over the top, then finely grate over the nutmeg and bake for 20 minutes. Leave to rest for 10 minutes, then serve (or chill and save for reheating later).