First, you need to roast the vegetables. Prepare the courgettes and aubergine ahead of time by cutting them into 1 inch (2.5 cm) dice, leaving the skins on.
Now place them in a colander and mix them with a rounded dessertspoon of salt. Then place a plate on top of them and weigh it down with a heavy weight, making sure you have a plate underneath the colander to catch the drips.
Leave them like this for an hour so that any bitter juices can drain out.
Drizzle the oil over, then mix thoroughly to get a good coating of oil. Roast on the highest shelf of the oven for 30-40 minutes, or until the vegetables are tender and tinged brown at the edges.
Remove from the oven and leave until cold.
Follow this with a sheet of filo, covering the remaining sheets of filo with a clean, slightly damp tea cloth. Brush all over the filo sheet with some of the melted butter. Sprinkle on a quarter of the nuts and Parmesan. Then do this another 3 times with the other filo sheets.
Then use the parchment paper to help you roll the filo over the filling and then over again. What you need to end up with is the seam and the ends tucked in underneath. You can discard the paper now.
If you want to, you can make the strudel in advance and bake it when you want to serve it. Or I sometimes cook it in advance and whack it back in the oven to warm at the same temperature for 10 minutes.