Trim and slice the aubergines lengthways into 1cm-thick pieces and place in a large mixing bowl. Drizzle with olive oil, season with salt, pepper and 1 teaspoon of dried oregano and toss together to coat the slices evenly.
Heat a deep 24cm ovenproof frying pan and fry the aubergine for approximately 3 minutes on each side, or until they develop a bit of colour. Set the aubergine aside, and don’t wash the mixing bowl as you will use this later.
Very finely slice the onions and fry in a little oil for 3 to 5 minutes, or until they colour. Remove from the pan.
Using the same ovenproof pan, spread one third of the aubergine on the base (be careful – it will be hot), followed by one third of the onions, then spoon over one third of the passata. Season with salt, pepper, the remaining dried oregano and scatter over a handful of grated Cheddar, then repeat with two more layers, finishing the final layer with extra cheese.
Cook in the oven at 180°C/350°F/gas 4 for 25 to 30 minutes, or until golden.
Break the lettuce leaves into the reserved mixing bowl (it should still have a coating of olive oil and seasoning from the aubergines). Toss to lightly season the leaves and serve with the parmigiana.