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Sprinkle both sides of the halloumi with the oregano. Heat the oil in a non stick frying pan, then briefly fry the halloumi on both sides until golden. Meanwhile, heat the flat breads over a naked gas flame for a few seconds on each side to warm them. (Alternatively you can do this in a large frying pan.)
Halve the peppers (removing any stray seeds) and thickly slice, then add to the pan with the aubergine and olives. Heat through, squeeze over two of the lemon wedges and season well. To serve, divide the mixture and the parsley sprigs between the wraps, and top each with a lemon wedge for squeezing over.