Preheat the oven to 180C Fan and set out a 20x30cm ovenproof dish.
Slice the courgettes very thinly using a mandolin - make sure you are following all the relevant safety precautions. If you don’t own a mandolin, you can use a very sharp knife and cut them into thin slices.
Add 1 tbsp olive oil to a very large non-stick frying pan set over a low heat and add the sliced courgettes. Season well with salt and pepper. Cook gently, stirring often, for about 8 minutes - or until the courgettes are lovely and soft.
Tip the courgettes into a sieve and drain off any excess water.
Return the pan to the heat and add 1 tbsp olive oil. Add the garlic and chilli and fry for about 30 seconds, stirring often, until fragrant. Add ⅔ of the drained, softened courgettes and season with salt and pepper. Stir to combine, then cook for a couple of minutes, stirring often.
Meanwhile, tip the other ⅓ of the softened courgettes into a blender. Add the crème fraîche, basil and a generous seasoning of salt and pepper. Blitz until smooth and creamy. Add about 2 tbsp grated Parmesan and blend again to combine.
Place ½ of the courgette ragu in the bottom of your chosen baking dish and spread in an even layer. Top with a layer of lasagne sheets. Spoon over ½ of the courgette-basil cream and spread to cover. Scatter with ½ the torn mozzarella (equivalent to 1 ball). Add a generous sprinkling of grated Parmesan. Repeat the steps - finishing with a generous topping or Parmesan.
Bake in the oven for about 35-40 minutes - or until bubbling and golden and the pasta is cooked through.
Leave to stand before serving with your choice of sides (I love it with a simple garlicky tomato sauce, a spoonful of ricotta and a drizzle of fresh basil pesto).