To make the dressing, gently heat the balsamic vinegar, olive oil and chilli together with 1 tbsp of water. Once warm, add the olives and the herbs, remove from the heat and set aside.
Bring a large pot of water to the boil, add the lasagne sheets and salt if you wish, then simmer for 3 mins. Meanwhile, heat the sunflower oil in a large frying pan until very hot. Add the flat cap mushrooms and fry for 1 min until they start to colour. Add mixed mushrooms and fry for 2-3 mins more. Season if you want to and set aside.
Drain the lasagne sheets and put one on the base of each of four large plates. Scatter the mushroom mixture over and put a second sheet on top. Spoon over the dressing, sprinkle over the parmesan and serve immediately.