Steam the onion in oil until translucent, add the aubergine cubes and bake for 5 minutes. Stir in peppers and tomatoes. After a few minutes, season to taste with salt, pepper and harissa. Cover and simmer for 20 minutes, stirring occasionally. Fold in parsley and let cool.
Preheat the oven to 200 ° C.
Place the puff pastry in the baking pan, prick in several places with a fork. Spread the aubergine mixture in the pan. Top with slices of mozzarella, sprinkle with Gruyère and Parmesan. Bake for 35 minutes. Let cool a little before serving.