Run the salt cod under cold water for about 10 minutes, then soak it in more cold water for at least a few hours (changing the water a few times), or overnight in a spacious container if that suits you better. If your cod is very stiff, it may need more help: after soaking, place in a pan of cold water and bring to a light simmer. Set aside and cool.
Preheat the oven to 200C/Gas 6.
Cook the macaroni al dente, according to the instructions on the packet, then drain and cool under cold water. Oil lightly to prevent it sticking.
Over a low-medium heat, melt the butter in a large saucepan and fry the garlic and thyme leaves for a couple of minutes before stirring in the flour. Add a little milk and stir well. Keep gradually adding the milk and turn the heat up a bit. Bring the smooth sauce up to a bubble, then turn it off and stir in the mustard and nutmeg.
Pick out and discard any bones and skin from the salt cod.
Now mix the salt cod and macaroni into the sauce until well combined. Season, mostly with pepper (easy on the salt). Check the consistency of the dish - it needs to be quite wet, as the macaroni will continue absorbing in the oven, so add a splash more milk if necessary.
Transfer to an ovenproof dish, sprinkle the top with the Parmesan, breadcrumbs and oregano and drizzle with olive oil. Bake for 30-40 minutes until golden on top and bubbling round the edges.