Pour boiling water over the spinach in a sieve or colander to wilt it. Leave until cool enough to handle, then squeeze out any excess liquid. Heat the oil in a non-stick frying pan over a medium heat, add the garlic and soften for 1 min. Tip in the nutmeg and cook for 1 min more, then add the mascarpone, spinach, half the cream and half the parmesan. Season generously, stir well and set aside.
Heat oven to 180C/160C fan/gas 4. Spread a third of the filling over the base of a 20 x 30cm baking dish, cover with 3 lasagne sheets, then add a layer of courgettes. Repeat twice more. Pour the remaining cream over the final layer and sprinkle over the remaining parmesan. Bake for 40-45 mins or until the sauce is bubbling and the pasta has no resistance when you push a skewer through. Rest for 5 mins, then serve.