Simmer tomatoes, oregano, garlic, and 50ml olive oil in a pan for 25 minutes.
Preheat the oven to 180°C.
Fry sliced potatoes in oil and butter until browned, then drain on kitchen paper.
Fry sliced aubergines until cooked and drain on kitchen paper.
Halve and deseed peppers, then fry for two minutes until slightly blackened.
In an ovenproof dish, stack potatoes into four piles and top with aubergine, pepper, and cheese.
Secure each stack with a cocktail stick.
Blend the sauce until smooth and optionally pass through a sieve.
Pour the sauce over the stacks and bake for 20 minutes.
Serve in wedges with a sprinkle of fresh oregano.