For the sauce, place the canned tomatoes, oregano, garlic and olive oil in a pan and simmer for 25 minutes.
Meanwhile, for the tumbet, preheat the oven to 180C/350F/Gas 4. Heat the oil and butter in a large frying pan. Add the potatoes and fry for about 3-4 minutes until coloured. Remove with a slotted spoon and drain on kitchen paper.
Repeat with the aubergine, also draining on kitchen paper.
Slice the two peppers in half, scrape out and discard the seeds, then fry for two minutes until slightly blackened. Transfer to a plate lined with kitchen paper.
In an ovenproof dish, divide the potatoes into four piles. Top each with some aubergine, a pepper half and a slice of cheese. Secure with a cocktail stick.
To finish the sauce, cool slightly before blending until smooth (using a hand-blender). You can pass the sauce through a fine metal sieve for a really smooth finish.
Spoon the sauce over the tumbet and bake in the oven for 20 minutes.
Serve in wedges scattered with more oregano.